Uniform Weapon Damage

I've used uniform weapon damage (really uniform attack damage, since monsters don't always fight with tools) for my past two B/X game sessions, and I like it a lot. I was worried at first that players would balk at their "normal" swords and two-handed swords being reduced to the damage range of a short sword or bow, but all of us greatly enjoy the simplicity. No fiddling to consult one's sheet for the strength of one's chosen method of attack; just find a cube and toss it. This also works nicely with the spells provided in B/X, since magic missile now does slightly more potential damage than most weapons.

But now... we've started moving to AD&D2. One key mechanic of both versions of AD&D is the two categories of weapon damage: one for small- or medium-sized creatures (or smaller), and one for large-sized creatures (or larger). For most weapons, this is a step down in die size - it's harder to take down an ogre with daggers than it is to defeat an orc, no matter how few hit points the former has. But for some of the larger weapons, the damage die actually increases. This presumably reflects that more force can be put into a warhammer blow when the target is easier to hit.

I like this mechanic. But how would I have it alongside uniform weapon damage? To retain the type of speed I get in B/X, I can't have both. I'm thinking I'll stick with uniform for now (unless the players unanimously want variable), and try out the differing damage types when they face a Large opponent.

A broadsword, or a magic missile?
Ultimately, it doesn't matter!
(Pic from the Japanese Rules Cyclopedia)

EDIT 2016-01-27: Well, I feel like an idiot. I've gotten so dependent on Firefox spell-check that I misspelled "broadsword" in the above caption. Fixed now.