maybe seems strange but my berdan cases are worth more than boxer cases. its the only way to use the berdan primer I have and berdan primed brass became more and more rare.
I bought 100 once fired 8x57IS military cases just to use my 5,5mm berdan primer.
resizing the 303 brass without anealing will be a hopeless game not to mention the fact this brass had a 1957 headstamp and was brittle only by the years it have seen.
think Winchester 303 is made by Sellier&Bellot, I have some of this cases and you can form 6,5x53R without problems. my 303 military brass have a very thick base, maybe 11,56mm so I turn it down to 11,43mm on the lathe. this is the base diameter of the 6,5x54MS die.