I'd suggest some kind of combined ELO if possible. At the very least, combined ELO incentives players to get good at more factions.
I'm not sure if your info is thorough enough for that.
I've wanted an actual matchmaking rating for a long time.
Yes when I came to COH I was surprised that there is NO global ELO. But when you think about it it makes sense in terms of how COH is played.
However I could imagine to have extra ELO for game modes, 1-1, 2-2 etc and another ELO for factions, Wehrmacht, USF etc ... That could be interesting - to see who is best Wehrmacht player across all the modes.
We could build whatever we want but we would need to have access to EVERY match. That's what other games provide - Dota 2, LoL etc, with their API you can retrieve latest matches. And when you have that you can calculate anything for the players.
COH2 have only API to retrieve matches for player. You can't get general matches. Which makes the whole data parsing extremely ineffective (you retrieve the same matches a lot from each player and need to filter it - and you need to know player ids beforehand). I hope that they will publish public API for COH3 with ability to get every match.
Because than a community can pick it up and build systems around it. When you look at other games they often don't even try to build their own thing. They just publish API, because they know others can spend additional time and resources to build amazing sites.