the Rema in 253 doesn not make any mention of lack of other food or other Tzorech Gadol.
Lack of any other hot food is tzorech gadol, that was actually Health’s case on which this discussion began.
Now I’ll answer your other question:
one opinion that food is more chamur. how do you know the Rema follows this opinion?
I don’t know it as a fact, I’m suggesting a reason that the R’ma does not allow cooking even l’tzorech gadol. If you have a better reason, kol hakavod, but clearly he assers it.
Please read my earlier post as well, which was not yet visible when you posted.