Wow...glad you figured it out. How does the socket go bad, just out of curiosity? Solder joints break?
Yup, and unlike the one on your MKII, the MKIII is a strange solder ball SMD type mount that requires specialized gear to fix correctly and not trash the plastic on the socket. The way i have fixed them in the past was to remove the CPU, clamp down the socket as best you can, then take a soldering iron to every single pin from the top and try to reflow the ball under it and not melt the socket in the process. Its time consuming and tedious as all hell.