Solved. Documenting what worked for me, for anyone who has the same problem.
Before I created the thread, I had done the research and it was clear the problem spanned years and distributions, and was sometimes reported as happening erratically. I was thinking initially it was looking like a driver issue, and then some kind of deep-guru hardware initialization/interrupt thing.
I verified this repeatedly:
From a power-down state, the boot freezes with “Initializing gfx code.”
However, if I have a running Linux instance, plug in the external USB hard drive, wait for it to be recognized, and then go to the root prompt and issue the “reboot” command, it works.