Problem being that so many AUs either do similar stories or just don't leave a lot of room for players to bring in a good variety of mobile suits, you know? CE is probably the one that has given the most room to tell both the Earth Alliance and ZAFT to sod it, considering just how hilariously insane both sides are, while still having a whole lot to do with third parties and MS to pick from, but then the issue is that pretty much every high performance machine is a Gundam.

So then if you're sticking to canon units you get the whole "everyone's flying Gundams", which to be fair is exactly how it goes in the shows, or you need to not allow them at all for players or allow for some degree of noncanon customizations for MS. If we're going CE my suggestion would probably be setting it after SEED but before Destiny.

There's about a year after the cease of hostilities and the signing of a treaty banning nuclear technology and mirage colloid as well as limiting MS production but before Destiny proper begins. During this time both sides were still stockpiling arms and advancing their MS tech, and it'd be the perfect time to conduct covert ops against eachother by hiring independents. Namely, the PCs. 

Edit: A potential issue with CE would be the supposed advantage coordinators have in literally everything ever over regular humans. But considering how the shows themselves don't paint coordinators in all that superior a light, if the players aren't dicks about it and its agreed the PC naturals are the gifted types like Lowe Guele then it shouldn't be a problem.