I’ve noticed too that drop target completions do not always enable the mode start. My conclusion too was that, to get the mode start enabled, you have to complete a new set of supplies. The PAPA rule sheet says this:
Food, weapons, and first aid will cycle. When one of the drop targets is hit, it freezes the cycle on whichever was lit at the time and you complete the drops to collect one of the three. This lights all available mode starts at the 5 main shots and the lights cycle once again at the drops.
But you may be right; it could be that it’s two bank completions for every mode start enable after the first one. If that is indeed the case (need to check next time I play it), then Bloodbath won’t automatically be ready after three mode starts, because it would be possible to keep completing already-completed drops, which would keep enabling the mode start, but not Bloodbath.
My apologies if what I suggested initially is wrong!