Oh, I also want to add that this is the EVT version of the board, and it's very possible there is some problem there, for example something leading to an over-current condition on this rail. I'm just hoping someone with experience with this part can point to some likely root cause for me to follow up on investigation.
I went back and looked at some oscilloscope captures that the board assembler sent. They did measure the current out of this thing. Based on the waveform I think they tapped into the circuit on the inductor (which goes from the SW output of the chip to the filter caps on the output). In a normal start-up cycle, peak current is 540mA, but during the failed startup cycle - the one with the funky sawtooth waveform on PG- there is a very brief spike of current to 2.78A, with corresponding output voltage of 560mV, before the output voltage and current drop back to zero.