you would have been better off comparing 762x54r to .303 british ( a lot of surplus russian got re load into 303 ), simply pull the bullet and powder then transfer to the .303 brass.
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No experience with .303 but surprised to read this as when I bought
bullets to reload (.308) they were sold as .311, I read enough to figure it could be done, I actually didn’t end up reloading myself and had someone else do it who was very skeptical but did it for me anyhow, I fired a few, worked fine, but .303 
Those British bores plenty shot out first?
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303 are actually .311
they both grow up roughly in the same school of thought (303 being a semi rimmed vrs 762x54r
most surplus 303 was loaded with cordite versus the powder in the 762x54r
normal surplus 303 was a thick gilding metal jacket, single piece lead alloy core 174 grain
303
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diving a bit deeper
it appears that Russia actually would take a live 303 round and convert it to 762x54r by reforming a loaded cartridge in a die.
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It’s a wonder gun people have avoided the transgender issues 
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