Well I fixed my problem.
I took it into the Apple store. Even without the other two monitors they were able to recreate the problem. One symptom (I had) was that one of the Hot Corners was set to Disable screen saver. If you then put your cursor there, you'd go into screen saver mode. Change the setting to another corner and the problem follows you there.
The Apple person at the Genius bar logged out as me and back in as test and same problem. He tried some stuff and finally said I needed to wipe the drive and reinstall the OS (Lion). I'd only had the machine for 12 hours and had just migrated my data to it, so I didn't mind doing that. I did it at home.
Problem solved.
BUT... then I reinstalled the driver for my EVGA UV Plus 19 (most current drivers) and bingo problem back. Uninstall. Problem gone. I'm now using mini display port to DVI for one monitor and HDMI for the other I think the machine is a bit warmer this way (versus using a USB to the EVGA device) but at least it's not sleeping all the time. Someone might say "it (the heat) is your imagination" or something else. Or someone might say "use the other thunderbolt port for another mini-display port to DVI" but I need that for the LAN... c'est la vie.
Maybe I'll write to evga and see what they say. Maybe they'll fix their driver and/or Apple will fix it.