The slaughter of innocent MPF-102s has ended (some victims are visible on top of the SPRAT). The culprit was NOT voltage spikes from the relay coil (although that might have contributed). Instead, what was happening was that I had the gate voltage set way too high on the transmit side. Whenever I powered up the rig, it was for an instant in the transmit mode (before the relay kicked in). The high voltage jolt on the gate was enough to kill the FET.
You can see the transmitter tucked in behind the relay. It moves my SWR meter on key down, so I'm confident I can get at least one QSO (perhaps across Rome) with this rig. Then, I intend to retire it. It will probably be a few years before I forget the pain and decide to build another minimalist regen rig.