We never did the 10 segment rounds. At the time, none of us grokked it.
We always used weapon speeds (as a basic modifier to initiative). It made more weapons relevant. 1E didn't really have many modifiers; adding a couple in didn't complicate anything as far as we saw. My Paladin in the Jade Regent AP had more modifiers to his rolls by 4th level than any 1E character of any level. As we didn't grok the initiative rules for spells, we just said that (in general) a spell had a combat casting speed of three times the spell's level.
We did use Weapon vs. AC Type, but it was only relevant when fighting humans, elves, dwarves, etc. Again, it kept more weapons relevant. A pick doesn't do a lot of damage, but it's at least decent vs. everything. As time went on, we fought more monsters and less human types so its importance diminished.
Technically, we did use psionics, but only one character ever had them and he died in his second adventure having never encountered a psionic creature.
We did use the racial level limits but they didn't really end up being very important. Nowadays, you've got AP's that run from levels 1-20, but you had nothing like that in 1E. There wasn't a lot once you hit the "lord" levels and most of those were either campaign enders like Tomb of Horrors or oddities like Barrier Peaks. Also, most non-humans were multi-class and so were behind the level curve anyway. We did use the suggestion (I think it was in the DMG, but I don't remember anymore) where you could advance further than the level limits, but it took double XP to do it.