I feel it likely that the person flying the plane wasn't aware of the ongoing handshakes between the satellite and the aircraft. Everything else was turned off - transponder, ACARS, no response to ATC. Why leave another form of "communication" alive - unless you were unaware of it.
So I think you have to assume a relatively constant velocity once established on the track south. If you believed you were completely "dark", the most important consideration was distance. The further away you got, the less likely you would ever be found.
Anyway assuming a constant velocity is already a difficult enough task. To try and calculate the effects of random changes during this final leg would appear pointless on the grounds of futility.
The recent comment about the inflight entertainment is intriguing. Things started to happen while passengers would still have been awake and some would have been watching flight path (or whatever moving map package was part of the IFE). So is may have been necessary to disable the IFE so passengers were unaware of the turn back. If so, that implies the turn back was very gradual. If on the other hand the plan was a steep climb with the packs off to disable the passengers, the IFE doesn't really matter. Why worry about the IFE if the passengers were about to be aware there was something wrong but would shortly become incapacitated. So something here doesn't quite fit.
The other thing is the passenger phones. I know some hear are sick of discussions about phones. But after 2 months searching I don't think we are in a position to discount any possible information that could aid understanding. A low level flight across Malaysia would have generated calls from any able passengers. And also handset registration with the phone networks from any phones left (on even if all the passengers were disabled at this point). So that doesn't make sense either. Possibly a phone jammer. Even an accomplice in the cabin could not have ensured that all phones were put in flight mode and / or turned off.
The other thing that would concern me as the pilot would be the chance that one passenger (and it would only take one) might have a sat phone on board.