don't forget a ?sinusoidal? rate of change if the TX crosses the concentric signal elevations.
I agree, this is what I meant by it gets complicated quickly. There's a lot of different parameters that can influence ping time beside distance alone.
Let me give a wild example that I personally witnessed a number of years ago in a related context. Someone had put a wifi relay in a tree with a clear line of sight to a bedroom window in the guest house. During the day the guests kept complaining of congestion on the line, despite the fact they were the only ones at home. It was a puzzle because the ping time got steadily worse during the day and then quickly recovered at night. A full wifi site analysis was done and no radio interference was found.
The culprit that was eventually discovered? The wind. Wait, how can wind affect the radio waves? It can't, directly. But what the wind was doing was blowing the small branches of the tree around. The location experienced a great deal of diurnal heating and as the heat increased during the day so did the wind and so did the amount of interference from the tree branches and so the ping time increased during the day and fell off at night in rhythm to the wind. The owner of the guest house had put the wifi relay in a tree because he felt it was unsightly and so long as there was no wind his plan worked correctly.
The point--radio waves are a tricky thing. In a normal situation there are not many causes of interference between an airplane at 35K and a satellite. But nothing about this situation appears normal. So I think it is something of a leap of faith to say that increasing ping times=increasing distance. It's a decent assumption but we've already seen how other reasonable assumptions have turned out to be wrong.
The Inmarsat Exec said the statement "the satellite wants to see if you still want service." That indicates to me that the satellite, not the SATCOM, initates the ping. It sounds like, after 60 minutes of silence, the Satellite wants to confirm that you are still on it's network. If you don't respond, it takes you off of its active device registry until you come back online and initiate contact.
Yes, that's the typical set up. I'd be surprised if it was any other way.