In AD&D, I've never used the weapons vs armor tables as presented. For a while, I used some home-brewed tables that give adjustments for each weapon vs four armor types: plate, chain, leather and none.
"You haven't had extensive weapons training but don't worry, you can get an exception to use the mechanically strongest godstat melee weapon. There is no page 149, your weapon choices are in chapter 3, and only one of them is right. Just take a rapier, and some daggers for fashion. Not to be used though."
Blanket proficiency in every weapon is a problem too, at least in the current system where there are a handful of best choices, and flavor becomes an exercise in justifying why your guy uses the best weapon while the rest of the common soldiers still choose long swords.
As far as weapons go, I've attacked this stupid non-system for a while but I always hit the dead end of "why bother, my PCs are a monk and a druid and won't interact with it," and then "everyone should just play a primary spellcaster and never use a weapon and then it doesn't matter" and I start trying to fix cantrips instead which just has me modeling them on weapons and...
I think one simple change you could make without rewriting the whole weapons table or combat system, is to give bonuses for switching it up. Dropping a heavy warhammer immediately after a staggering hit and drawing two quick short swords for the followup sounds cool, and I want my players to do cool things. Off the top of my head I would think changing damage type, handedness, ability score used, and light-heavy spectrum could all have an effect on combat. Even switching from a strength thrust with a rapier to a dexy fencing technique should overcome the penalty of switching from str+3 to dex+0.
Going the other direction, you could give the enemies a bonus for using a weapon that the PC is unfamiliar with, and enforce that by having their blanket martial proficiency atrophy if they never pick up anything but a halberd for months on end.