I found out, after a ton of debugging, that the board refuses to POST without a monitor attached. Not without a GPU - I have one in there, a discrete GPU (7900 XTX), but the board simply refuses to POST. Plug in HDMI and it is magically fixed, but this is not a reasonable solution for me.
One possibility is that it's really the VBIOS that's getting upset with no output, rather than the motherboard BIOS. If you have another GPU available (ideally something other than a RX 7000 series), you could try swapping it out to see if you get the same behaviour.