The 7600 with the hard butt plate will rattle your cage at least as badly as the Ruger 77. Not knowing what you are hunting, I don't know exactly what to recommend. There is nothing in the 7600 pump that will reduce recoil over a bolt gun. I'm not sure about the 750 auto, but Browning's BAR in .30-06 is surprisingly comfortable to shoot. The auto action on it absorbs an amazing amount of recoil. Maybe the Remington autos do too, but I haven't personally shot one to be able to say.
I really like the 760/7600, but recoil reduction is not in it's bag of tricks. Do not expect it to be easier on you than the Ruger 77.
The synthetic stocked model has the R3 on it so that might be easier on you than the traditional wood stocked version.
If you are deer hunting at reasonable ranges some of the "managed recoil" loads might be worth trying.
EJ