I am not a bullet maker (yet). Matter of fact, I just started reloading, but I have done a lot of soldering and brazing in my trade.
Regardless of what type of flux you are using, you only need a scant film on clean brass to make a bond. Maybe you could get a round wire brush and mount it in a hand drill to score/clean the inside of the cases for flux prep. Then make an oversized Q-tip (also sized to snugly fit inside the prepped case) that is just damped with liquid flux. That way you get a thin, even film of flux inside the case before the lead is set in there.
Interesting thread, BTW.