Because you're par-cooking and holding you've got a couple of problems. One is soggy skin, and the other soggy crust.
The skin gets soggy from your par-cook method and low temperature (pretty much the same thing).
The sogginess is coming from water on the skin, which is then penetrating the batter. When the chicken is cooked in the oil, the moisture turns into steam and "steams" the batter from the inside.
The chicken skin must be absolutely dry when it's breaded.
In your case, even though you're using a breading procedure, you're actually making a sort of batter by holding the chicken breaded for as long as you do. Worst of both worlds.
You could modify it by freezing instead of refrigerating; but I'd expect it wouldn't do a great job for the crust, and introduce a lot of other problems as well -- like toughness, and cooking all the way through.
If you want to continue par-cooking, the best answer is probably holding off on the breading until just before frying; and that should solve your problem -- at least for the crust. You'll still get flabby skin underneath, but at least the crust should be crisp. I often fry chicken which has been par-cooked in the smoker (smoking is almost as bad as steaming when it comes to flabby skin). From a texture standpoint, it's adequate and not ideal.
I don't know if par-frying chicken would work. Par-frying works with some things, but I've never tried it with anything breaded. I'd be afraid the crust would break from all the expansion and contraction. Worth trying.
While you haven't said what temperature you hold your oil at, fried chicken and other breaded foods crisp at a fairly low temperature. You can fry at 325F, and indeed many people do to insure that the crust doesn't burn while the chicken cooks through. But again, a higher temp is worth trying. What can it hurt?
I think most chains which don't pressure fry (KFC Original) or "broast," simply bread raw, then deepfry. Deep fried pieces should take less than 10 minutes, and not 20 to 30. It's pan frying which takes awhile. You might consider deep frying if you aren't already.
Paranthetically, you can fry chickent at a fairly low temperature (as low as 325F) and still get crisp breading and skin. (Relatively) low temp frying is often done to make sure the breading doesn't burn while the meat cooks through. You'll want to fool around with temp until you find whatever works best.
Good luck,
BDL