There hasn't been much discussion on BTD here. Likely a consequence of, as you say, cart-before-horse thinking. However, with strong P2 results, I'm thinking we're a shoo-in for BTD. Per the FDA:
Breakthrough Therapy designation is a process designed to expedite the development and review of drugs that are intended to treat a serious condition and preliminary clinical evidence indicates that the drug may demonstrate substantial improvement over available therapy on a clinically significant endpoint(s).
...
Ideally, a Breakthrough Therapy designation request should be received by FDA no later than the end-of-phase-2 meetings if any of the features of the designation are to be obtained.
Given our involvement with CTAP from the beginning, followed by Fast Track, BTD seems the next likely step in the process. That is, of course, if P2 results warrant accelerated development. Fingers crossed.