The rifle was built for Spain and was made in 1893, like the model, there was also a model 1895.
The best thing to do is make a chamber casting and then measure the casting to determine the chambering. The 303 is a rimmed case and the 7x57 is rimless. They would not fit in the same bolt and using a round in a gun that it is not chamberer for is very dangerous. The material you need for the chamber casting can be purchased from Brownells, this is a link to the product.
I hope this helps,
It sounds like you have a headspace problem, the chamber should be checked with headspace gauges after doing the casting.