After replacing the fuel solenoids on both CATs and still experiencing the same issue, I replaced the 12-volt relay in the electrical box with guidance from FW & Barlow in NZ. The problem has not resurfaced in 10+ years.
Barlow and I caught up for a beer last week as I recently acquired his 450 from another CSR member. I'm now the 3rd NZ owner and she is still in immaculate condition. It's great to be able to talk to former owners about the history.
The jumper lead for the fuel shutoff solenoid is still in the engine room for emergencies along with a spare 12v relay.
I'm not sure why the relay cooks itself. Possibly arcing "fuses" the contact points in the relay. Presumably a solenoid coil can discharge when power is removed (back EMF, I think it's called) and this might cause a problem over time.