I looked through the linked Arch documentation and tried some of those suggestions, replacing nouveau with radeon because I have an AMD GPU, but that had no effect.
Unfortunately, there is no toggle to disable the dedicated GPU in the BIOS either.
I tried adding radeon.modset=0 rd.driver.blacklist=radeon video=vesa:off in grub as suggested here but that had no effect either.
On non-Qubes Linux I use the MUX switch provided by asus-linux/asusctl but it depends on asus-nb-wmi which has been deliberatly omitted from Qubes for security reasons.
I feel like the answer is right in front of my face, but I can’t see it.