The GPS takes the four strongest signals. At altitudes above 70K it may be confused by having six or more with equal strength and two or more may be very low on the horizon. The system gets what it sees as an impossible solution.
There's no particular reason for any of what you've just said. I have a hand held that supposedly can track 12 satellites and I've not noticed it get confused. The more satellites a GPS can see the more alternative solutions it can make.
There is a limit on altitude and speed for GPS but that is artificially mandated by the US Government to stop them being used for ballistic missiles. I suggest they might have made an exception for their own aircraft.