At your level, knowing what sort of pawn formations your chosen opening is likely to lead to, and knowing what typical middle-game plans those pawn formations call for, is far more important than memorizing specific sequences of moves.
The Opening for an Average Player?

At your level, knowing what sort of pawn formations your chosen opening is likely to lead to, and knowing what typical middle-game plans those pawn formations call for, is far more important than memorizing specific sequences of moves.
Yes, I agree. So I've looked over Soltis' Pawn Structure Chess, which is great. Know of any other similar things?

Pawn Power in Chess by Hans Kmoch. It's a great book, and you'll get more out of it each time you re-read it.

"The problem is that I almost never, in any of my games, end up (and by "end up" I mean after 7-10 moves) anywhere near any of the main lines,"
It's normal. "Main line" for non-master players is the c3 Sicilian, KID/Benoni, and d-pawn openings like the London.

That's ok, of course, because what would be the point of both players playing scripted moves on cue? But it makes me wonder just how deeply I should bother studying any of the openings until my playing strength improves. It seems that for opponents at my level it's more a matter of 'play the natural moves' rather than 'rely on opening theory to get you a solid position for the middlegame'. And so I find myself questioning the value of spending time on the openings, beyond basic familiarity (where "basic familiarity" looks something like: 'Ok, in this Semi-Slav-ish position, I'll be looking to position myself for an ...e6-e5 or ...c6-c5 break, with play down the relevant file once it's opened').
Thoughts?
I think you're right.
Preface
I'm an average player. I spend most of my chess time (aside from playing) studying tactics and playing over master games. I'm in the 'you should do some opening study even as an average player' camp for various reasons, though I don't think it's necessarily the most important thing on my road to improvement. But I make time for it.
What do I play?
As White I always play 1.d4 (it feels natural to me, and I like closed or semi-closed games, so). I've mainly looked over the QGD and Slav/Semi-Slav complexes, although with how often I find myself facing the Nimzo-Indian, I'm about to work on that a little bit. As Black, against 1.d4, I usually play the Semi-Slav. Against 1.e4, I play 1...c6, 2...d5 aiming at something Caro-Kann-ish.
So what's the problem?
The problem is that I almost never, in any of my games, end up (and by "end up" I mean after 7-10 moves) anywhere near any of the main lines, or even main variations, of any of the above. I usually wangle some kind of Semi-Slav-ish-looking position when I face 1.d4 as Black, but play rarely follows any of the lines.
That's ok, of course, because what would be the point of both players playing scripted moves on cue? But it makes me wonder just how deeply I should bother studying any of the openings until my playing strength improves. It seems that for opponents at my level it's more a matter of 'play the natural moves' rather than 'rely on opening theory to get you a solid position for the middlegame'. And so I find myself questioning the value of spending time on the openings, beyond basic familiarity (where "basic familiarity" looks something like: 'Ok, in this Semi-Slav-ish position, I'll be looking to position myself for an ...e6-e5 or ...c6-c5 break, with play down the relevant file once it's opened').
Thoughts?