I was trying different things to fix the problem, and I seem to have resolved it.
I shut down the computer and unplugged ALL my USB devices while it was powering down, and unplugged the power before it could turn itself back on.
Plugged all the USB stuff back in, but I swapped the wifi and bluetooth this time. When it booted back up, the bluetooth wasn't recognized by Windows. So I shut the computer down... And it stayed off!
I've swapped everything back to its original location, but the problem seems to be totally gone, at least with my computer PSU. I'll try it with the M2-ATX later tonight.