> I lobbed on dielectric grease to clean electrical connectors between a right-angle C13 cord semi-permanently fixed to the receptacle on my Zero DSR and it still melted to crap.
Dielectric grease does *not* clean contacts. You need electrical contact cleaner for that. Dielectric grease prevents water ingress and further corrosion from that source but it doesn't clean up any resistance-inducing material or corrosion that is already present.
> As for where to find replacements, I'll keep buying the "3ft 14AWG Right Angle Power Cord #7683" from Monoprice when mine melts, which it is want to do from time to time.
Those are good. 14awg is good, or 12awg to be even safer. If you have access to 220vac, it halves the amps so thinner capable would be ok.