Hotel Tango. You say that
any problems the crew may have encountered.....could have been any time after 02:48
That's true. But the point is that we have no evidence as to when, or even if, such problems did occur in that time. On the other hand, we have fairly strong circumstantial evidence that something was going wrong during that last 2 minutes and 40 seconds before the "the flight signal was lost from radar", as the Hellenic CAA put it. That's because, during that time, 804 was not responding to repeated calls from Athinai ACC.
39 minutes earlier, the CAA says
The pilot was jocund and thanked in Greek.
What that surely suggests is that this was not an instantaneous event that immediately incapacitated the crew. It was, rather, something that caused the crew to be taking some kind of, perhaps desperate, action during those 2minutes and 40seconds - and perhaps for longer than that.
Edited to add:
....or I suppose it could suggest that the crew had been incapacitated, and that, for those 2 mins 40 secs, the aircraft was flying itself.