Mt Al,
The fact that it is a side x side may be contributing to the problem. When the rifle barrel heats and the shot barrel doesn't, the point of impact will change. I will also do this with an O/U or a drilling, but a SxS is the worst. Try this, set the target and fire one shot. Take the target home and do the same thing the next day (or week). Take the target home again and return the next day (or week) and shoot the third shot. If you are not satisfied with a three-shot group, repeat the exercise until you have the number of shots in the group you want. You can do it all in one day, but you have to wait longer between shots than you think would be necessary. The object is to have a "dead cold" barrel when you take a shot. Also, don't rest the barrels in the V, put your "off" hand in the V and hold the guns forearm, if a barrel is touching a solid object, it will shoot "away" from that object. It goes without saying that you should first do what fuhrmann suggested with the addition of holding the gun and scope up to a light source and see if you can see any light betwee the rings and bases, as well as ensuring the "slider" is fully seated. More than likely, if hook plate is moving in the dovetail, the whole group would move, not individual shots.
It seems that you have experience shooting groups or for score with different type rifles, but hunting is a different game; you don't win with the smallest group or highest score, you win when you put one bullet in the right place every time even when you are cold, sleepy, and need to pee.
Good luck,
Mike