The RN's 6pdr is not a direct replacement for the Army's 6pdr, but a gun that should've been manufactured instead of the 2pdr. Thus, it looks splendid.
Instead of the Army's 6pdr, they need to start designing the tank-going 3in gun.
FWIW, you're in esteemed company, sort of. A A.G. Williams suggests in AN ALTERNATIVE 1930s BRITISH TANK GUN to adopt the naval 6pdr ammo (with slight changes), but to design a new gun around it to take advantage of higher pressures made possible by contemporary propellant. With a steel core APCR AP performance estimated to be slightly better than the 2pdr, but substantially better HE. And later on as the steel core APCR runs out of steam, it's possible to introduces a tungsten core APCR with something like 50% better penetration. And substantially more compact than the historical 6pdr AT gun and ammo, so might better fit into early war tanks.