I play Semi-slav solid but dynamic. Suits my style, like the French
1.d4 openings and repertoire

Just a note - the Queen's Indian, English Defence systems, and the Nimzo-Indian share significant ideas in piece placement and general strategy. You might want to try those together for some flexibility?

You could choose the one that White players are least likely to know, or that is the least work for you? Or just pick the one in which you have the best results. Or if you are a fan of some player, play what he does.
What was the reason for eliminating those that you did?
Also of that list I'd recommend the KID because it leads to the most tactical games, and that's what you should be looking for at amateur level.

The most solid while maintaining chances for Black would be the NI/QID complex. The most versatile would probably be KID. Grunfeld and Slav would be second choices or change ups. QGA while acceptable has limits in applicability if White forgos c4. Dutch can work but be prepared for its weaknesses to be exploited as you move higher up the food chain. Semi-Slav, forego any thoughts of a life outside of chess if you wish to master it.
Some idea of your playing strength would help.

You have spent an entire year playing every defense possible against d4, I have spent entire life playing every possible defense against d4 and only found dissapointment, not OTB but in computer and game analysis.
But at last I can say that I have found what I'm looking for, a defense that is applicable in the highest level of chess, and more more so in the amateur level. And it's the QGA. Strangely, QGA is not well analyzed while I found that many lines are playable. I believe it will just need time for this defense to become more popular in the near future.
I'm still studying this defense and the related openings such as Catalan, Reti and QGD to understand more about the defense and get the best possible repertoire.
Currently my pet line is adopting Alekhine ideas, focusing on creating an isolated queen's pawn with ...c5. And I have analyzed a few games related to playing against the IQP.
Yes, I'm still studying opening variations where White delays c4 such as 1.d4 d5 2.Nf3 Nf6. It may transpose to other than QGA but I cannot find no reason why I should not play the 1...d5 against 1.d4.

KID, Grunfeld, Slav/Semi-slav, QGA, Dutch, NID, QID.
I have eliminated with certainty: QGD, Benoni, BID, Chigorin's, Benko Gambit
I think I can understand your elimination. Now look at it this way. There are theoretically "weak" openings that will give you complicated positions or petential for complications. This makes things fair because both sides has high probability of making mistake. But imo it is not wise to choose this kind of opening unless you are in GM level. Especially if you play in rapid tournaments.
With 1.d4 Nf6, if White opens a possibility to play the saemisch or at least kingside fianchetto, I think it is wise to transform to Gruendfeld with ...d5.
The semi-Slav, I think it is theoretically losing but it is like the KID, I like playing it because I know that my opponent will not play it perfectly and I will have my chance. But playing such defensive positions in rapid games is too risky.
NID/QID is higly theoretical. There are so many variations. I even have my own pet lines you cannot find in the database. But I have difficulty playing the indian type of games in fast time control. And playing as White, I will certainly avoid the NID/QID and play the Catalan, so you have to be prepared playing against it.
The most solid while maintaining chances for Black would be the NI/QID complex. The most versatile would probably be KID. Grunfeld and Slav would be second choices or change ups. QGA while acceptable has limits in applicability if White forgos c4. Dutch can work but be prepared for its weaknesses to be exploited as you move higher up the food chain. Semi-Slav, forego any thoughts of a life outside of chess if you wish to master it.
Some idea of your playing strength would help.
This helps a lot. My rating, based on Chessmaster, is around 1400. I have yet to join the USCF, so I cannot give you an actual rating.

Can't believe I'm helping a Wolverine but since you're stuck with Rodriguez I should take pity on you .
In tournaments, at your level, anything you know will generally work for you. If you know the opening and its ideas you can handle deviations from the book caused by:
1) Ignorance by your opponents (you might know the first 15 moves, he probably knows three).
2) Those of greater strength who have "pet" ideas or subvariations to bypass opening prep. e.g. When I was a 1200 player a few decades ago, I played a very strong 1900. I was using the French then. He uncorked an idea he'd been working on. It was wrong for the French but not in the books, as I discovered later. I beat his novel idea, gained a winning advantage and threw it all away when I overlooked a tactical shot. He got the point but as he confessed in the post mortem, I won the game. I didn't have main lines memorized out to 10+ moves but I had played over many, many games and thus was comfortable when my opponent went off the reservation. ML are such because they are the best. If someone deviates from the ML the onus is on them to prove the correctness of the change. His opponent needs to find out why its not ML and take advantage of it.
So, slightly modified opening suggestions: Don't take up the KID yet. Despite its versitility it can be a strategically subtle line where timing of pawn breaks, etc is crucial. Stick with the NID/QID complex. The Bogo is fine as well, and easier than the QID but you've eliminated it for whatever reason, so be it. Look at the Dutch as your change up. If you know for sure your opponent will play d4/c4 QGA is also good. At club level you see more d4/Nf3 games. If you want to screw with your opponents mind play:
1.... e6 then you can follow up with 2.... f5 or 2.... Bb4+ just be prepared for 2. e4 and you must look at the French with 2.... d5 or get really strange with 2.... c5 hoping for a e6 Sicilian but prepared for a Franco-Benoni 3. d5 ....
Hope it helps, best thing to remember is play the game, have fun, grow stronger, win more. In that order.
Can't believe I'm helping a Wolverine but since you're stuck with Rodriguez I should take pity on you .
In tournaments, at your level, anything you know will generally work for you. If you know the opening and its ideas you can handle deviations from the book caused by:
1) Ignorance by your opponents (you might know the first 15 moves, he probably knows three).
2) Those of greater strength who have "pet" ideas or subvariations to bypass opening prep. e.g. When I was a 1200 player a few decades ago, I played a very strong 1900. I was using the French then. He uncorked an idea he'd been working on. It was wrong for the French but not in the books, as I discovered later. I beat his novel idea, gained a winning advantage and threw it all away when I overlooked a tactical shot. He got the point but as he confessed in the post mortem, I won the game. I didn't have main lines memorized out to 10+ moves but I had played over many, many games and thus was comfortable when my opponent went off the reservation. ML are such because they are the best. If someone deviates from the ML the onus is on them to prove the correctness of the change. His opponent needs to find out why its not ML and take advantage of it.
So, slightly modified opening suggestions: Don't take up the KID yet. Despite its versitility it can be a strategically subtle line where timing of pawn breaks, etc is crucial. Stick with the NID/QID complex. The Bogo is fine as well, and easier than the QID but you've eliminated it for whatever reason, so be it. Look at the Dutch as your change up. If you know for sure your opponent will play d4/c4 QGA is also good. At club level you see more d4/Nf3 games. If you want to screw with your opponents mind play:
1.... e6 then you can follow up with 2.... f5 or 2.... Bb4+ just be prepared for 2. e4 and you must look at the French with 2.... d5 or get really strange with 2.... c5 hoping for a e6 Sicilian but prepared for a Franco-Benoni 3. d5 ....
Hope it helps, best thing to remember is play the game, have fun, grow stronger, win more. In that order.
Thanks again Carl, this is also helpful. Having not yet played in an official tournament, this helps to know what to expect.
And yes, there should be a mercy rule that all opponents of Michigan should abide by when conversing with us Michigan fans. I'll call it the Rodriguez Mercy Rule. We didn't want him, but the boosters did and as you know, money talks.
I should also say that against 1.e4, I have chosen the French, Caro-Kann, Scandinavian, Petrov's for certain (and maybe the Spanish or Pirc, but doubtful).
Also, what think ye of the Grunfeld? It seems to fit with my play in the French as far as "feel" even though the structures and themes are different.
I didn't pick BID because at that fork in the road (3.Nf3) I prefer QID.
QGA would fit well with my Caro and Scandinavian choices, and with the Slav, but there is just something about it that I don't like, and I really don't know what that is yet. It just doesn't feel comfortable despite its simlarities to the aforementioned.
I really like the Dutch and its affinities to the NID/QID and French, but seems best as a secondary suprise opening and not a primary one.
I enjoy the KID a lot!; but it has a lot of similarity to the Sicilian and Pirc (or even the Benoni)as far as structure, none of which I really care for.
If I could master any opening against 1.d4 it would be the Slav. There is something so appealing about it, but I don't know what it is yet.

If you play the Caro or 2....Qxd5 Scand, play the Slav. Too many simularities not to. I got into the Nimzo cause I played French Winawer, same concept. Everyone played 3. e5 so I dropped the French but started working with the e6 Sicilians. Go for QGA as the switchup for the Slav. Grunfeld is OK, I prefer Nimzo.
If you're going to play KID, look at Acc Sic Dragon for Black. Again affinities between systems.
For CC/turn based: Play them all. Use a basic opening manual/dbase to keep the basic moves straight and play them all and have fun with them. Only for OTB, assuming you have a life, restrict your choices and study time to openings you can play for life. Nimzo, QID, KID, Slav, etc. Don't waste time becoming a specialist in say the Englund. You'll win games from those that don't know it or panic but it will hurt you in the long run.
PS Look close at my avatar. GO STATE!
PPS I married a Wolverine.

How does the Dutch avoid theory? There is plenty of theory on it, its just not in fashion right now.
I would appreciate some help in deciding on what my repertoire should be against 1.d4. I have spent an entire year playing every defense possible against e4 and d4, and with e4 have had no problem narrowing down my choices based on style, what naturally fits, personality, results, etc. My problem with 1.d4 is that the list of candidates I have narrowed it down to is more vast. I assume this is because I prefer the d4 openings in general. My list is:
KID, Grunfeld, Slav/Semi-slav, QGA, Dutch, NID, QID.
I have eliminated with certainty: QGD, Benoni, BID, Chigorin's, Benko Gambit
Any ideas you may have or new angles of approach you can suggest to help me narrow down to 3 or 4? I realize there are significant differences in style between the options I listed, but my problem is that these differences do not make a big difference in my play as much as the same dilemma does with e4 defenses.
Thanks for your time!