i am leaning towards the first part of Greater Divine Surge working, but if you have no Con score or are immune to the Con damage (which btw are completely different from each other), then you cannot take Con damage to increase the spell's power.
but if you heal your Con damage that you actually take, then obviously it would work.
that is different from corrupt and divine spells, due to it being a choice when the spell is cast. kind of similar to paying extra power points to augment a psionic power.
but this same argument would mean that, corrupt and/or sanctified spells cannot work since you cannot satisfy to corruption or sacrifice cost. like trying to cast a Curse of Lycanthropy without having an animal's blood (obviously eschew materials would change that).