I find the King's Indian as a solid response, as long as you know the correct lines are comfortable with using it. I also recommend, at a lower level of play, to stick with one or two solid responses to common openings like 1. e4 or 1. d4, instead of memorizing many different ones, as the middlegame and endgame are much more important to focus on, and just playing the same openings over and over again is fine until you get to a higher level of play.
What is your favorite non-symmetrical 1.d4 opening for Black?

1) d4 b6 the English Defence
2) d4 a6 the St George Defence
3) d4 b5 the Polish Defence
4) d4 e6 the Horwitz Defence
5) d4 e6 c4 Bb4+ the Keres Defence to try to transpose to a Bogo-Indian or Nimzo-Indian
6) d4 c6 to try to transpose to a Caro-Kann or Schlecter Pirc or Slav-Indian Defence
7) d4 f6 to transpose to a Neo-Mongoloid Defence after e4 Nc6
8) d4 c5 the Old Benoni Defence
9) d4 a5 to transpose to a Ware Defence or a Snagglepuss Defence after e4 Nc6
10) d4 h6 to transpose to a Carr Defence after e4
These are the responses I would play against 1.d4!

after 1.d4 e6 2.e4 there are two good options either 2.a6 the French St George Defence or 2.Nf6 the Mediterannean Defence

11) d4 h5 to transpose to the Goldsmith Defence after e4 or the Picklepuss Defence after d4 h6 e4 Nf6

after 1.d4 e6 2.e4 there are two good options either 2.a6 the French St George Defence or 2.Nf6 the Mediterannean Defence
Neither of those are good

11) d4 h5 to transpose to the Goldsmith Defence after e4 or the Picklepuss Defence after d4 h6 e4 Nf6
Nobody in their right mind would play h5 seriously.

The stuff we do to avoid that dreaded London System... I prefer the Caro-Kann against 1.e4, but I'm pretty clueless on how to play against 1.d4. Anybody have a favorite?
I know how you feel which is why I troll with the Englund Gambit sidelines for speedy time controls; throws out the London System on move one and no theory to learn:
https://www.chess.com/game/live/36736772221
https://www.chess.com/game/live/20569756995
https://www.chess.com/game/live/19202809479
https://www.chess.com/game/live/19202809479
My two main lines which are imbalance and must win scenarios are the Modern Defence and KID.
Preferable the Modern-Pterodactyl line in hopes of transposing to a Sicilian Hyper Accelerated Dragon (I’m a Sicilian player):
https://www.chess.com/game/live/36570632453
If I don’t get my pterodactyl/dragon line, KID is straight forward:
https://www.chess.com/game/live/35347608319
https://www.chess.com/game/live/16431939425

As a 1d4 player, I have to say I really dislike playing vs the Benoni. There's seemingly only one 'good' way to play against it, and it's not what I wanted out of playing 1d4 at all. I'm yet to come across the hippo' in a game. I'm not looking forward to that either.

1.d4 Nc6!
2.d5 Ne5 is fun for black. Even strong guys play bad moves here that lead to alot of perpetuals/forced wins which just need to be memorised by black. E.g. 3.e4 e6 4.f4 exd5!! Is the most common sequence of moves at 2500 level on lichess and is just an immediate draw by perpetual.
2.c4 e5 3.d5 Nce7 4.e4 Ng6 is my favourite position in all of chess. I think I score over 80% here
2.Nf3 e6 3.c4 Nf6 is a transposition to the Tango, and 3.e4 d5 is a funny version of the French which is considered aggressive for black
Every other move is met by the break 2...e5! The good thing about 1...Nc6 is that it stops white's nonsense by preventing the Colle, Stonewall, Veresov, Jobava etc. and discouraging the London and Tromp.

King's Indian is good but as black you have to be careful or else you can easily get a very cramped and uncomfortable position, with a king that can potentially be exposed. The advantage is, of course, that you can get a solid attack going on the flank towards white's kingside (assuming he castles short). A lot of thematic moves and ideas in the KID may also seem counter intuitive.
Personally I think the KID is effective against certain setups white can do, like the London and King's Indian Attack, perhaps even the English.
I have tried the Queen's Gambit and Semi Slav, but I think the Queen's Indian and Nimzo Indian suit my style better.

The stuff we do to avoid that dreaded London System... I prefer the Caro-Kann against 1.e4, but I'm pretty clueless on how to play against 1.d4. Anybody have a favorite?
Since you already play the Caro-Kann, I would recommend you play the Semi-Slav. It doesn't look too intimidating at first but it has a lot of venom and it's great when you get the Botvinnik Semi-Slav (my favorite opening) created absolute chaos on the board but loads of fun. If you want to learn more, I recommend you check out my Semi-Slav study and Sam Shankland's Free Chessable Course
The stuff we do to avoid that dreaded London System... I prefer the Caro-Kann against 1.e4, but I'm pretty clueless on how to play against 1.d4. Anybody have a favorite?