I recently flew on Air New Zealand flight 28 from Auckland, NZ to Houston, Texas, USA. This flight crossed the southern part of the Baja Peninsula and northern Mexico, slightly north of the great circle passing through these airports. This flight must have gone right through the middle of your "no radar" zone.
Elapsed time between wheels up and wheels down, using my wristwatch's "chrono" (stopwatch) mode, was 13h15m57s, about 8 minutes less than the predicted flight time announced at the beginning of the flight.
The outbound flight (NZ 29) a few weeks earlier was about 90 minutes longer, and we were aloft for almost exactly the announced time at the beginning of that flight according to my watch. The portion of that flight over North America was dark and mostly cloudy, so land features could not be identified once we left the Houston area.
Google earth reports the great-circle distance between the airports as 11934 km, giving the effective average ground speed as about 820 km/h for the outbound flight and 900 km/h for the return, but the actual ground speeds must be at least a little higher since the actual flight paths must be longer than the great circle path. This seems consistent with the stated cruising speed of the Boeing 787 used on this route, 567 mi/h (912 km/h), considering winds aloft, reduced speed at take-off and landing, and true distances flown.
Any questions?