It may be worth mentioning that the F-80 Shooting Star was unable to exceed Mach .96 under any circumstances, verified by NACA wind tunnel testing.
The chances that an Me 262 exceeded Mach 1 are nil. Even the F-86, a genuine transonic fighter, could barely exceed Mach 1 (Mach 1.09) in an extended dive from 35,000 feet.
My regards,
Widewing