^I believe you misunderstood the last paragraph. By "a variant of Burning Godzilla", I don't mean them "changing" Burning Godzilla from a plot device built around his death (which I agree should be left alone BTW) to a "powered up", Super Saiyan-esque form of Godzilla, and thereby deriving from the essence of "the" Burning Godzilla, I meant a powered-up form that clearly draws inspiration from it, but is not strictly Burning Godzilla, basically pays a little homage to it. One idea I had is having blue ultraviolet rashes glowing throughout his body in place of the glowing red/orange lava rashes.
This would be a nice rendition for the third movie and way to close out the series, especially if G2 has all 3 of the confirmed monsters in it (and I've seconded everyone's "I think they will be because them not doing so after revealing all 3 in a teaser for the film will result in huge backlash" sentiments on here myself) and they planned on bringing Destoroyah in as the big bad to close out the series, and they could add MechaGodzilla (the last remaining kaiju in Toho's "big 5") to the mix in order to make it happen, too (the "transformation"), I see it playing out in one of two ways:
A) A Godzilla & MechaGodzilla vs. Destoroyah film: Godzilla teams up with the robot created in his image (for the very first time) to battle the abomination created from his and his original foe, Shinomura,'s DNA (my take on an origin for a Legendary Destoroyah) after initially being blamed for the unforseen damage caused by him, basically starting out as a Godzilla vs. MechaGodzilla film until Dessy arrives.
B) A DAM remake featuring both MG & Destoroyah plus an assortment of other monsters (it could perhaps include a few new ones from Legendary/Gareth as well).
In both scenarios, the "secret project" they were building from the Godzilla cave skeleton in G2 (which was set 4 years after G14, meaning it took years to make) finishes construction, built to protect the public from future monster threats or Godzilla should he emerge as a threat himself. Destoroyah eventually emerges and completely obliterates Godzilla in a one-on-one confrontation (just to show what would happen if Godzilla tried fighting Destoroyah without his added power boost in GVD), almost killing him (sound familiar at all?), leaving the humans to mourn his loss and turn to the mech created after him. MechaGodzilla battles Destoroyah and seemingly wins until he secretly reforms himself after vanishing and destroys MG from out of nowhere. The humans then use a hybrid copy of his fusion reactor to "supercharge" Godzilla after injecting him with its radiation via cables. Godzilla then marches after emerging from the base stronger than ever and battles Destoroyah again (I'm thinking NYC for a choice of location) and beats him this time in an epic fight, a very Dark Knight Rises esque vibe to it (think Batman emerging from the pit to get his revenge on Bane after getting trounced by him and the humans cherishing his return).