For me this looks like there has been failure situation / slow decompression or problem with Oxygen for crew, they might have started diversion, altitude change, possible some issue with the Avionics, I don't know the T7 systems, so can't comment on details of this.
At one stage they have BOTH become incapacitated, and descended in altitude, flown on until running out of fuel (Similar Helios)
What exactly caused this to happen, none of us can only speculate in, but what is important is to create the most likely scenario and work with this.
Most such scenarios it will the most simple and least spectacular version that will be the truth.
The problem with this though is it conveniently ignores some parts of the data that just don't fit. Such as the voice radio transmission sector change acknowledgement AFTER the transponder was shutdown, etc.
Unfortunately it doesn't seem what is postulated is the simplest solution to all the information that we know, even if that answer isn't one that we'd like it to be.
Coming up with a half-baked hypothesis (and I'm not trying to insult anyone here) and suggesting the plane flew off in the murky blue yonder for 7 hours or so until it flamed out, doesn't seem to fit with the last radar track point and the INMARSAT ping arc.