Looking at the specs on the PSU, it seems the cables I'm worried about provide a maximum of 150W. With the 6990 supposedly vetted for up to 475W, I think I'll probably be safe. I'm going to switch on the machine later and I'll let you guys know what happens, just in case someone else ends up having the same questions I did.Edit 2:
Dug through the PSU box one more time in an attempt to find something useful before embarking on an experiment which could fry my video cards and found two 6 to 8 pin adapters. Put those on and powered up and... well, three long beeps and no signal from the video cards. But the fans were spinning and I'm pretty sure the cards are alright. I tried to get a signal from a third card of a different model and still wasn't able to get anything.