Okay, I've done a little debugging and it seems to be a bug in the
Intel UXA drivers. I switched to SNA and all three monitors work fine
now.
I added the following lines to a new file in /etc/X11/xorg.conf.d/20-intel.conf:
Section "Device"
Identifier "Intel Graphics"
Driver "intel"
Option "AccelMethod" "sna"
EndSection