cherrybim: I’ll respond to the substance of your arguments, but not to your crude style.
Igros Moshe is not a sefer of theoretical logic, for that look in Dibros Moshe. Igros is Reb Moshe’s psakim halacha l’maaseh, and he writes that turning down a flame is NO BETTER then turning it off. If turning the fire off is already muttar, as you maintain, why bother??? It doesn’t need to be better, only the same.
Additionally in the context of his other 2 teshuvos on the subject. Reb Moshe’s intentions are self-evident. If it is anyways muttar to turn off a gas range because of gram kibuyi, why does he need to write at length (to his grandson, who certainly qualifies as a “family member”)that it is “better” to turn down an existing flame l’tzorech ochel nefesh than to light a new one, if turning down the flame is muttar l’chatchila not just “better”??? Also, why delve at length into the idea of melacha sh’aina tzaricha l’gufa, if there is anyways no melacha involved???