The first part of Rav Belsky’s teshuva is consitent with the IG”M 8 I showed you, that it’s talui on the minhag. I don’t know why he only relied on it b’tziruf his other sevara (1:45).
The latter part of Rav Belsky’s teshuva ignores the reasoning of the poskim who have a problem with chasnus of a mumar; it’s no better than an aku”m without children, with whom bishul is still assur (I think I saw it in the Lechem Haponim).