I just don't get the weird confusion about AD&D rules. Especially if you're just talking core books + a few supplements, it's a fairly rules light, easy system that holds up very well today, tossing and modding a rule here or there.
I don't ever recall players being confused, back when 1st and 2nd were in print, about things like whether a Saving throw penalty is described as +4 (to the save) or -4(to the roll), or that AC was hard to understand. So I wonder if the confusion is more for people who didn't/haven't played any edition up through 2nd, and particularly exclusively CRPGers. Because I believe AD&D is far less "byzantine" in practice than modern legend would have it. It's complex, and runs better in PnP watered down IMO, but its just not the obscure beast it seems to be portayed as from time to time.
If it helps, maybe look at AC as a modifier to an enemy's attack roll, as relative resistance -
Saving throw priority? A bit obscure, more of a DM thing, but a straightforward mechanic.
Ability checks do roll under on d20, but they're not core until 2nd, and there are good arguments to not using them much. Even so, it was't confusing. OMG I want high on attack rolls, but low on ability/ NWP checks!? IT'S BYZANTINE!!! *brain implodes*