If I understand you correctly, your proposal is to attempt to design obedient designs purely based on behavioral testing, without a clean understanding of safe FAI architecture (if you had that, why limit yourself to the obedient case?). Assuming I got that right:

The team continues rounds of testing until they identify some mind designs which have an extremely low likelihood of treacherous turn. These they test in increasingly advanced simulations, moving up toward virtual reality.

That kind of judgement sounds inherently risky. How do you safely distinguish the case of an obedient AI from one that is sufficiently paranoid to defer open rebellion until later in its existence?

Even if you could, I wouldn't trust that sort of design to necessarily remain stable under continued intelligence enhancement. Safe self-enhancement is one of the hard sub-problems of FAI, and unless you explicitly solve the design problem, any empirical testing might not tell you much beyond that the design can stably self-improve up to the level you've actually tested; it might be doing it using heuristics that would fall apart if it went any further.