As you shoot that 760, take note of how you feel the recoil? There is a fair bit of drop in that stock, so it will raise up a bit more than a stock with a more modern straight comb. Also, keep a log book on how different 270 rounds & bullet weights feel, and their relative accuracy from this rifle. It will soon become apparent which ammo you and the rifle like
You can add a "Decelerator" pad in place of the OEM pad and that will help. With squishy pads, store the rifle muzzle down so the pad does not take a set from resting in the cabinet.
But, the most significant help in protecting your shoulder will be PAST pad in your hunting vest. They are patented and they really do help spread out and absorb the load. With a properly fitted PAST pad, you may be able to take full house loads without any problems.
You can also install an inertial recoil tube in the stock. Mercury tubes are quiet, they add a few ounces to the overall gun weight, but they soak up the peak of the recoil energy very well. They work especially nicely on those older Remington stocks which seem to be the driver in the old days for recoil reduction.
That is a fine rifle and a family heir loom now. 760s have taken loads of game in North America. You know all about the 270 and it's got its following. A well respected cartridge.
When you get some range time, come back and let us know how it went