Yes, that's correct. Pushing the derailleur in, towards the wheel/spokes/largest cog, it won't go all the way over. I guess if my LBS would do a free assessment, I might just ask them.

As for how long it's been going on, not exactly sure. To be honest I'm not positive it ever worked correctly, but have just recently been getting more into doing my own maintenance and thus became more aware of it.

And it's definitely the L limit screw, as they're marked, and also if I shift the RD all the way in (where it should be on the lowest gear), loosening it does nothing while tightening it moves the derailleur to the right. So it seems the limit screw works, just not in the way I'd like it to, which would be moving it inward toward the wheel a bit.