I think I'm going to find the IC heating up, given that it developed an internal short. I could get an IR camera to pinpoint what part of the IC is hot but is this going to be valuable info? Or are you suggesting some external part of the circuit may also be heating up and that could be the root of the whole failure?
I believe, based on your description, that there was an issue on the board and when increasing the power available to the IC it was able to destroy itself. I am suggesting that the failure was on the board external to the IC. The internal short was likely a secondary failure caused by the first.
Using continuity (with audible beep) mode on my multimeter, probing at the nearest connected component (e.g. C4) on the same net so that I don't have to get the probe on the very fine pitch IC pad. I skipped checking for shorts between a pin and adjacent NC pin, maybe it's not a safe assumption that those aren't internally connected to something?
I would suggest using resistance mode just in case you have a higher impedance short that would not give you an audible continuity beep. NC pins are defined as not carrying a bond wire to the die so I believe you made a good assumption not checking them.
I would suggest trying again. Bring it up to 4 volts and check some waveforms, I am hopeful with that information you will find the issue and be up and running