Measure a cost-quality curve and test a cascade

Record every model's answer to every register once, then do all the analysis offline. The cascade needs no new calls: for each register you already have Haiku's answer, the strong model's answer and the verifier's verdict on Haiku's, so the cascade is a lookup. The decision that matters most is measuring the verifier on Haiku's real outputs. Its recall on those, not on mistakes you invent, sets the cascade's error floor $e_s(1-R)$.