Looks like someone needs to go work with these guys for a day.
One other thought... Are these saws put thorough any kind of break-in after they are rebuilt or just handed over to a saw jockey to run balls-to-the-wall. This might help explain your immediate rebuild failures. Adding more heat since they are not broken in might push them over the edge. I have broken several 260s and have definitely noticed a decrease in friction / increase in idle as the saw breaks-in. Older saws that run richer might be able to handle more break-in heat / abuse than these newer ultra-lean saws.
One more thought... Pre-ignition is caused by too much heat, too low octane fuel, or ignition timing too far advanced. Have you checked timing advance on a rebuild and compared it with another no-issues 362? Other way would be to swap out a coil just to rule out coil going wonky advance when it gets hot. These ignition modules have CPU processors in them which may not like the high temperatures that they are exposed to and go wonky when overheated.
One more thought... How are these carbs being setup? Are you tuning them for max RPM at shop temperatures (70F)? If so they will get considerably leaner at colder temperatures as the cold air is more dense. If I am tuning a saw at higher than the lowest likely operating temperature I usually leave it a little rich to account for this effect.
My $.03,
Steve