Actually, your quote is selective and out of context. Reb Moshe in 4:60 was only lenient on a Shabbos clock, not a true Amira l’Akum. Furthermore, he explicitly differentiates between lights where there is already a Minhag to be lenient, and he is not capable of forbidding it, and other appliances. He clearly writes that it is wrong to rely on the Itur and the Minhag in Europe was to be stringent.
He would NOT permit your crockpot where there was no Minhag to be lenient.
“The Psakim I quoted comes from Piskei Hilchos Shabbos Vol. 3 & 4” “C’mon, it’s in Vol. 4 which wasn’t even printed till 1990”
You also mentioned vol3, which is where I checked. I didn’t see the context of his rulings, but you mentioned bathroom lights. When the generator broke in my son’s Yeshiva, HaRav Shteinman ruled that bathroom and stairwell lights are Pikuach Nefesh. If the Debretziner agreed, his Heter would not be relevent to a typical Tzorech Gadol.