Honestly, setting it after CCA is... Problematic. The Sleeves weren't a major military force, more a terrorist group. They had minimal manufacturing base, and only really began as a group nearly two years after CCA, just in time for the Laplace Conflict. And they basically dissolved to rejoin the Federation following the Laplace Conflict, which really only took place between the Nahel Argama and Frontal's crews. There's just almost nothing between the end of CCA and the start of Unicorn.

So, to be perfectly honest, you'd really need to either dedicate yourself to going mostly AU following CCA or set things during a time where the greater conflict isn't so defined. The Gryps Conflict and First Neo Zeon War were both pretty small scale in terms of what we saw; the Argama (and later Nahel Argama) were only parts of the overall conflict. We, for example, didn't see much of Karaba versus the Titans on Earth or any Federation forces versus Haman's Neo Zeon. That era could work pretty well.

If you do go AU, I'd advise carefully thinking out who you use for a villain. Delaz was never really a follower of Zeon Zum Deikun's philosophy, he was really just a revenge obsessed ass with a grudge to settle. That's why he had basically no plan past "We're gonna colony drop the Feddies again". 

I'd also probably advise looking over the general state of mobile suits in the UC; while I can see why you would restrict Gundams for the most part, a lot of them actually have mass produced counterparts. And most of the Gundams, unlike in AU Gundam series, aren't inherently all-powerful mobile suits. The pilots are the OP ones. The Zeta and Double Zeta both had true mass produced counterparts made by Anaheim, and even grandaddy RX-78 had some derivations produced in limited numbers. And almost all of those Gundams (RX-0 not included because the Unicorn really is ungodly OP in a Newtype's hands) were either matched or completely [i]out[/i]matched by mobile suits in their same series. The O was a beast of a mobile suit, for example, that Kamille could only beat due to Newtype hax.

Long story short, you might want to consider carefully what era you set it in, and who you use for your antagonists.