Ok, a bit more experimenting and this looks like a different problem now.
I do in fact get a picture, and it is indeed a 15kHz 60 hz picture as expected. And I can turn on the Dreamcast and see a picture WITHOUT the PC also being turned on first.
BUT, over the course of about 30 seconds to 1 minute the picture slowly fades away and goes to black. After that I have to unplug everything, let it sit for a while, turn it all back on, and same thing happens.
Looks like a cap somewhere is charging up slowly and then squelching the signal. That or my ground is floating and slowly rises to the point that my effective RGB signals go to zero. No ideas beyond that. Anyone else have any pointers here ?