But wait, there's more...
I just dug out the 28 July 1942 Wright Field memo asking to use the designation XP-78-NA for the "new" North American Fighter, Interceptor. Washington responded on 20 August:
Classification as Experimental is approved for the P-51 Airplane with Packard Rolls-Royce Merlin 61 engine installed. It is most desirable that the production airplane be given a model designation which will definitely identify it as one of the P-51 series. Although the different engine definitely changes the performance of the airplane, it will still remain basically a P-51. Due to the work which the British are carrying on with this airplane and engine, and the very optimistic view of the project held by Materiel Command, the classification Limited Procurement might well apply and is hereby approved provided the airplane be called P-51 with an appropriate suffix added.
By command of Lieutenant General Arnold.
That doesn't clarify just why the P-78 designation wasn't accepted, but at least we know who made the decision.
Cheers (again),
Dana