The Browning .303 used British made amunittions, as it was the same cartridge as in the normal Army riffle, so easy to produce. The weapon was based on the US Browning .30, but addapted to take in the British .303 round. Having a seperate US model round for an non british weapon was too much to ask for in the 30's, as the time simply was not good to make such a move, given the priorities then.
I agree the Hurricane could easily carry six Browning .50's in her thick large wing, although weight would be problematic. It was even thought to put six larger 20mm guns in at first, but that was luckily not proceeded with, as the penalty in serious reduced flightperformance was too big. In the end, the wing only had two .303 mg's and two tankbusting 40mm guns under the wing.
By the way, the shooting down of german aircraft with .50 cal guns is not at issue, only that you need to use more rounds to do the job, where a single larger shell could do it more easily. The FW-190's in the Wild Boar variant, with heavy armor and heavy weapons (Some FW-190 variants used the standard two 7.92mm mg's and four 20mm, to which they added two wingpods with and additional two 20mm's each, for ten guns in all. Flightperformance was not too great logically, due to the overloaded status, but these could bring down a B-17 with a short burst only. If you had only .50's, you need to empty your magazines to bring down one B-17.)