If the rifling looks fine, but you can insert a round at the muzzle end and it fits all the way up to the case then the muzzle is certainly worn.
But...maybe the remainder of the barrel is still tight?
Push a cleaning rod through with a tight fitting patch (from the breech end).
If the pressure needed to push the rod through is firm but 'suddenly' feels loose up near the muzzle then you need to figure out what distance from the muzzle does the loose bit start.
Then cut the barrel shorter and recrown it at that point.
Might solve all your problems quite easily.
I have seen an old .303 rebarreled to .444 Marlin.
Don't think you are restricted to only finding a .303 barrel.
Lots of options, just the amount of $$ might not make sense.
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