If the fire was severe enough to incapacitate the crew I don't think the plane would have flown as far as it did.
Fire was put out, if there was one, or as you say plane would have crashed much earlier if airframe was compromised by fire.
Fire in a sealed container, like a pressurized aircraft, uses up available oxygen pretty fast, so can be self-extinguishing, and if it was a fire, then oxygen masks can't be deployed for the obvious reason of not giving the fire more "fuel".
Oxygen depletion also extinguishes people
While dealing with whatever crisis was happening on this flight the Autopilot would have been engaged once a new heading was set, so all hands could deal with crisis.
And without the option of using oxygen masks the lack of oxygen or high carbon monoxide levels incapacitated the flight crew..........autopilot still engaged.
Whatever happened was first noticed and assessed, just before the change in heading, new heading was to closest long runway airport , autopilot was then re-engaged for this new heading, so pilot and co-pilot could deal with problem.
The only two facts that seem to be indisputable are the course change and that the "pings" continued until on-board fuel was exhausted.
Fact one fits with closest airport
Fact two fits with autopilot engaged and no one on-board conscious or alive