My early 2011 MacBook Pro just started having the exact same issue. I encounter the same graphics artifacts you do. I can tell you what does not work:
- Snow Leopard
- Lion
- Mountain Lion
- Different Memory
- Different Hard Drives
- Different Power Adaptors
- NVRAM Reset
- SMC Reset
The only thing I have found to keep the system stable is using gfxCardStatus to force the Intel GPU to remain active. The issue with this is sometimes the system will end up crashing before gfxCardStatus loads. I would love to find a permanent solution which did not involve replacing the system board, but I have pretty much lost hope at this point.