Problem was US made HS404s rarely worked as intended, though US makers never adopted the shortened chamber that solved most of the issues that the British initially had.
Of course, on secretprojects I've read that the USAAF wanted eventually to mount 4 20mm cannons on the P-51H and the P-82B/XP-82, but NAA said "nope". Of course, if there's any truth to that on either end, I can say that NAA did propose armament fits for the P-51 and A-36 that included 20mm and 37mm cannons or a mix of the two, per several posts made my drgondog when discussing Mustang armament fits. But each time NAA proposed anything other than .50s, the USAAF ignored them.
Thus if the USAAF wanted 20mm cannons on the P-51H or the P-82B (due to both aircraft's potential as interceptors with 5000+ fpm climb rates on normal max take off weight and WEP), and NAA told them no (story is that NAA spec'd out for 6 .50s on both planes already when the USAAF suggested it), North American had been burned before on doing such work expecting/hoping the USAAF would come around to the cannon armed P-51.
And yes, If you've read the chapter about the P-51H in Michael O'Leary's book "Building the P-51 Mustang", there were mock ups of the NA-117 (pre-production P-51H design, production models were the NA-126, with the P-51L being the NA-129), there's photos there (as well as probably in Boeing's archives, and maybe someone else's archives) of a P-51H mock up with 4 20mm cannons.