I'm reconsidering it now, as it's been in the back of my mind all this time. I printed up and re-read the man-to-man rules, and I think that those should be enough for grunt level humanoid vs humanoid combat. I also read through parts of the Grey Elf's Compleat Chainmail Combat System pdf. It's a collection of clarifications, house rules, and design notes from the Grey Elf and others for using Chainmail combat resolution in OD&D.
The explanations in it helped me to get a better idea of how to run Chainmail Arena.
I've still got to figure a few things out. If I use the man-to-man tables for humans/demi-humans/humanoids, that's fine. Using the fantasy table for fantasy creatures is fine. But when normies fight the fantasy creatures, it seems to require the normal Chainmail mass combat resolution. I'd like to simplify things so all rolls are 2d6. Hopefully, this pdf will help clarify things. It seems like it will.
So this game is closer to happening than it used to be.
Addendum: I've watched a video with an example of play, and read more of the Grey Elf pdf. I'm thinking now that abandoning the man-to-man table might just be easier. Instead of recruiting individual goblins or whatever, players will recruit humanoids (and normal animals) as packs/squads.