Leftoverdj, I'd say the chances of his rifle being rebarreled or rechambered is pretty good, seeing as how the rifle in question is an 1891 Mauser, and the 308 did not come to life until the 1950's. Winchester and Rem made both rifles and ammo for this chambering until the mid 30's.
Critical dimensions are close in both rounds.
7.65 Mauser 308 Winchester
Case Length 2.10 / 2.810
Case heads are the same at .473
Shoulder dia. .429 / .454
Case head to sh. 1.76 / 1.56
Never tried it, but I don't think you could get a 308 to chamber in a 7.65x53. If you could, the accuracy is not going to be all that good as the 7.65 is a bit larger in diameter, .313, although .311 or .312 diameter bullets are said to be satisfactory
Drdirk, you might try a small base die-I know RCBS makes them. They squeeze the brass down a bit farther. Would be interesting to know exactly where your full length resized brass is hitting the obstruction and what it might be. Do you have any fired cases from this rifle which have not been resized? If so, check the dimensions of the fired case vs one you have resized. That should give you an indication of what is wrong.
The other option is to shoot some factory brass thru it and neck size only. If you are worried about pressures, and I would be too, I'd be tempted to pull the bullets on the factory cases and put in your lighter powder charge.