This could also explain the climb to 45,000 feet if the plane was on auto pilot and the fire was messing with the instruments.
The Pitot static systems (which are redundant) on a 777 are very far aware from the transponders. So this fire that magically spread all the way across that, somehow allowed auto pilot to have enough elevator control, change the engine power, but not realise it was hitting the ceiling, then was able to calmly decent from an above service ceiling height?
Incredibly unlikely set of events.