In Mongoose Traveller, some weapons have a recoil number. I like that implementation, since it allows you to fire a big gun and then that recoil number adds to your initiative next turn. Simple, and effective. Now imagine if there was an easy way to use those pesky weapon speed factors from 1st edition AD&D? Maybe there is.
How about you do the same thing? Sure, initiative is a very different beast in AD&D but considering how many hacks of that system there is, yet another wont make much of a difference.
So, roll 1d10 for initiative. Then add that weapon speed, and count up from 1. You could probably use it both with individual and with group initiative. One size fits all, eh?
Let me know if you try it, or have already tried it out. I think is sounds neat, on paper at least.