Thanks for the suggestions for solving my booting problem, which admittedly
is not particularly Gentoo related at this stage in the installation
process.

I’ve tried usb sticks with both Sysrescue and Ubuntu server to boot this
thing.  It appears to attempt to boot each one, but then the screen goes
blank after 1-2 seconds, at which point I can’t tell what’s going on.  Each
usb stick boots my other machines normally, and the screen works normally
when used as a display for my other Gentoo machines.

Your suggestions imply that there’s nothing especially magical about
putting Linux on Asus mobos and that I’m setting up the bios correctly.  So
I’m coming to the conclusion that this mobo may not be working as
intended.  Back it goes!

John