I’m very pleased that my paper has led to such a rich exchange and that it has brought out the importance of clarifying one’s aims in the ongoing development of set theory. Insofar as it might affect my draft, I still have much to absorb in the exchange thus far, and there will clearly be some aspects of it that are beyond my current technical competence. In any case, I agree it would be good to bring the exchange to a conclusion with a summary of positions.
In the meantime, to help me understand better, here is a question about HP: if I understand you properly, if HP is successful, it will show the consistency of the existence of large large cardinals in inner models. Then how would it be possible to establish the success of HP without assuming the consistency of large large cardinals in V? If so, isn’t the program circular? If not, it appears that one would be getting something from nothing.