Sorry to hear about this. One of the big downsides to turbine flying is fire and the potential to lose literally everything. Sounds like the pump kept pushing fuel into the turbine after the flameout...

You mentioned "extinguisher up the exhaust"... FWIW, you should always fire the extinguisher down the intake, that way any burning fuel or gasses are directed out the steel tailpipe, not back onto the flammable interior of the jet. Also, you want a C02 or halon derivative (i.e. gas), not a chemical or dry extinguisher - chemical extinguishers should be considered a last resort, as any electronic or metal items will be damaged (dry chem agents are very corrosive).

Again, sorry to hear about your loss!

Barry