Tartare - just a mild kick on the needle as you accelerated through the Mach, I think you have the physics nailed. Other than that in the cockpit it was the biggest non event.
Over the seas IIRC it was 10 miles heading away from the coast or 30nm parallel or inbound towards the coast to go supersonic (or was it 35?).
For the 2 ATAF boys it was over 36000 feet and then game on.