I'd only use the water clearing stuff every 2-3 days to be safe. Those are usually fairly benign chemicals intended to cause the tiny particles to clump together and get caught by the filter and back when we had gravel there were times i used AccuClear daily without any ill effects on the fish.
I'm not sure that any of your current tank's residents could go in with cichlids.. maybe the loach and snails, but i'd see what the cichlid owners say on those 2. the livebearers, gourami and tetras would mostly likely die in a tank of cichlids. i'm not certain on the ADF but i don't think it would be a happy tank for him either.
You could seed the new tank with filter media or gravel hung in pantyhose in the new tank to hopefully speed that up on cycling.