I'd have it rebored to .35 cal on the 303 Brit case.
Simple and requires no alterations to keep it feeding & extracting/ejecting.

I had a BSA Lee/Speed done over to the cal and a (Watson Bros) Martini Sporter also. Both had burned out .303 bores.

JES Reboreing did the work for me.
Excellent work, more than fair prices and a fast turn around of a couple of weeks.

http://www.35caliber.com/

I loaded the round on 35Remington dies which I already had .
It made excellent shooters out of a couple of sideways lead throwers with little effort.
Not quite as classic sounding as a .375 whatever but they worked just fine.

He can do a .338 or .375 on the 303 case too.
.35 just seemed a good fit as I had a good supply of bullets already from my 35 Remington and Whelen shooting.

Call Jesse. Leave a msg if he doesn't answ,,he WILL call you back.He doesn't always hear the phone ring with the machines running.