I don't have a 760 or a 7600, but I still hunt with the earlier Remington 141 pump in .35 Remington. In general, pumps will give you the same or better accuracy that you would get with the semi-auto rifles. If you use a pump shotgun, transitioning between the two is simple. Like the other poster said, they are big in PA. Amish Machineguns is what a few of my relatives back there call them. And if you look around on gunbroker, you will probably be able to track down some of the more unusual variations through some of the dealers back there. Limited runs of things like .300 Savage, .35 Remington, .35 Whelen with blonde wood, that kind of stuff. But pretty much everybody I know back there that uses one has a .30-06. Something as common as .270 should be fairly easy for you to find.
