Hello99,
Even if he were not a da’as yochid (as I suspect he’s not, based on IG”M, and based on cases brought in R’ Yitzchak Zilberstein’s sefer on amira l’akum in which he’s mattir a d’oraiso (kavod habrios is one – he is mattir having a non-Jew fix a toilet if water cannot be brought in), one still cannot extrapolate from one case to another. The Mogen Avraham says this regarding a shvus (307:7) and it would certainly apply to a d’oraiso.
The R’ma in 328 allows bishul al y’dei aku”m for a child who has no other food, because a child has a din of a choleh. If the R’ma were mattir a d’oraiso for the mitzvah of oneg Shabbos, this would be true even for a healthy adult.
I’m not sure how you learn R’ Moshe’s refrigerator teshuva that you don’t agree that he was mattir a d’oraiso for a specific tzorech gadol, but I certainly agree that he would not be mattir bishul just because you need a cholent for Shabbos.