243ackley,
You didn't post photos of your and your friend's guns, so this is speculation. A combination gun that has the barrels soldered together may act like yours as a result of one barrel heating up and lengthening while the other barrel does not. Some Krieghoff drillings have "free floating" rifle barrel, but I don't know about the O/Us. The maker of your friend's gun is known for making their products with a "free floating" barrel, to avoid this. This problem is more severe with SXS combination guns than O/U. The answer is when sighting your rifle in, to let it cool to ambient temperature between shots. As a hunting rifle, it is not important that it shoot a small 5 shot group with out cooling. What is important is that it put the first shot where it should, every day. The 7x65R is a world class cartridge and you are not likely to need a second shot. If the animal doesn't "fall at the shot" you aren't likely to be able to reload in time to get a second shot off. If you have the time, in the off season, and range facilities, it is good to sight the rifle in by firing one shot each day( not absolutely necessary if you let it cool). Of course this assumes the scope and mounts aren't defective in anyway.
Mike