Like I said, whether I let the monitors autodetect or whether I explicitly selected DVI, I wasn't getting a signal. Also, in response to your point about DVI-I not working if it's connected to something digital on one end and analog on the other, both ends were digital.
In any case, I've figured it out. I plugged in all the DVI stuff and rebooted, and everything worked... apparently rebooting is important to tell the video card to produce a digital signal. I knew it was something stupid I was missing.