All correct and good answers to your question, Sarg. The only way to know is to measure, then you know for sure. Standard .303 brass can be thinned to about a .010" wall if using an outside neck turner. If is indeed well oversize, opening the chamber to 8x57R is the way I'd go. The muzzle shows a very thin rifle barrel wall.

I'd work at restoring it's inner surface (lapping or polishing as the 'need' may be) to allow descent shooting - cast or jacketed. A 215 to 220gr. cast bullet at up to 2,200fps will do as much as what the gun was designed for. There are excellent specialty mould makers, LBT comes to mind, as well as lube producers, LBT comes to mind. Last chart I saw, was $125.00 for a DC mould made to your specs.