It's good thinking. I'll take a shot.
I think if the props on both planes are nearing 450 TAS and running inefficiently, you must fall back to the drags of the planes themselves. We know that the wing loading on p47-22 is greater than fw 190A. We also know that fw190A out turns a p47-22 based on the fan plots. So, I think we can conclude that the p47 is simple more aerodynamically streamlined for diving (less draggy) and this is why it eventually catches up and surpasses the 190A in a dive. I don't think the p47 prop all of a sudden gets more efficient when it breaks the sound barrier, but I could be wrong about that. Anyway, it is not the weight of the p47, but more so that the 190 wing simply generates more lift and that creates a drag. Yes, there is a weight difference. But if both planes were shaped as same sized spheres and one is twice as heavy as the other, I think you won't get that much separation.
Also ot, don't ever dive after a p51 in 109. Climb, pursue and hope he turns. If he is diving away from his home base, you have him. Simply cut off the angle.
