My first XBox 360 - the one I just recently resurrected from the Red Ring of Death - died again. After several weeks of use, the graphics and sound started getting corrupted after a few minutes of play, then finally just gave me the RRoD on startup. But I brought it back to life once more!
This time, I did things slightly differently. I had noticed when I reassembled the 360 that the heads of the bolts now holding the heatsinks to the motherboard end up being pressed fairly hard into the bottom of the case, thereby causing some warping of the motherboard when it was fully attached. So I enlarged the holes I had previously drilled in the inner metal and outer plastic lower case, making them large enough to allow the bolt heads to pass through.
Second, rather than heat up the GPU while its heatsink was relatively loose, I first loosened but then tightened it as much as I dared, then performed the overheating operation. In my case it wasn't necessary to independently cool the CPU to extend the overheating period: with no fans attached, at power on I got the three rings, then about three minutes later this changed to two rings, indicating CPU overheating and shutdown. During this time, both heatsinks got very hot. I allowed everything to cool down, attached the fans and shrouds, and now it works perfectly. Yay!
UPDATE 2009-11-12: My nephew found at least one situation where the CPU overheats - at Mass Effect loading screens. When I was fiddling with the motherboard during my latest fix efforts, I handled the mobo by the CPU heatsink, which probably loosened the heatsink very slightly. So, I tightened the CPU heatsink a tiny bit and now it seems to be okay.