Just my two bits but it sounds like it takes more rounds than anyone is likely to shoot while hunting to make those groups really open up, and even then its still hitting bullwinkle.
I wouldn't worry about it.
I would install a limbsaver pad though. Makes the length of pull a half inch longer which may be too much depending on the good dr's size but it does cut back some of that recoil. Were it mine, I think I'd prefer 7mm-08 to 7mm Rem in that rifle anyway, but the Limbsaver pad helps