253 is just Mokom Mitzva while everywhere else is Mitzva Gemura.
There’s no difference. If you have another cholent, it’s not any sort of mitzvah, it would be like the “peiros” which is not muttar even with a double shvus. If you don’t have another cholent (or, more accurately, no other “tavshil cham”, then it is a “mitzvah gemurah”.
I know that it’s assur because we don’t generally hold like the R’ma, and I feel that the R’ma wouldn’t be mattir here anyhow. You, l’shitoscha, backed yourself into a corner by agreeing with hello99.