Would sticking a DVI cable to the monitor in the 2nd GPU, and sticking an HDMI cable to the same monitor in the 3rd GPU work the same?
Yes it would, and I have done that in the past.
I now use a KVM.
If you happen to have enough monitors in your place, you could temporarily attach them to the GPUs prior to start up. Once you are in windows, you can then remove all the monitors you don't want to use on that system and put them back where they came from (wife's PC, Kid's PC, etc). Now windows will see all your GUPs even though they have nothing plugged into them
KVM ftw... 1 monitor, 1 keyboard, 6 GPUs