I should start with the disclaimer that I am not knowledgeable in the Extended Universe/Legends canon. But I am a lifelong Star Wars fan and have been enjoying both Imperial Civil War and Ascendancy.
My suggestion is this: for all or at least the first few eras of the FotR GC, limit the locations from which you can produce clones. Because the Republic is still relying on local forces in the first era or two, and because the clone army is still growing, any clone units can only be produced on Kamino (and a few other worlds, if that's too hardcore/unbalanced). The trade off would be that those worlds produce clones very quickly. This could include vehicles typically piloted by clones, or with a visible clone trooper crew (BARCs, etc.), or a less disruptive approach would be to only limit the production of clone infantry units to these locations.
These restrictions could be relaxed automatically through era progression, or indirectly by unlocking a clone training center at Era 2 (or whatever's appropriate), which players could build on planets where they wanted to produce clones.
Obviously a problem with this is getting the AI to make use of this mechanic/not trip over itself because of it. However, I think you ought to consider it in some form in order to encourage the use of local military forces by the Republic in the early game.
Thanks for all your hard work!