This is an interesting thread and I enjoyed following it so far...
But: why is a Captain (or the rest of his crew) of a transport category aircraft unable to calculate the maximum allowable flight-duty
and ensueing rest-time by himself?
Even if the flight has been crossing several time zones.
That's the kind of stuff I was asked to do for both my European and FAA ATP written test - many years ago.
I don't understand. Am I missing something here...?