I shoot only pre'64 M/70's, my front rest is a Frankford Arsenal plastic model to which I have added a Protector leather bag. My rear rest is a cordura bag similar to the one in the pic, with this equipment I am able to shoot MOA groups most of the time.
First thing I would check is all of the scope mount screws, the ones attaching the bases to the rifle and the screws in the rings. Clean the threads on the screws and the holes with rubbing alcohol or acetone, apply removable strength Loc-tite and re-assemble securely (I don't worry about torque). After the scope is secure check the front and rear action screws, they need to be tight. The middle action screw just needs to be secure, overtightening will put the action in a bind. The screw in the barrel boss just needs to be snugged up, don't overtighten. With those things done shoot a three shot group, pay attention to the position of the forend and sling swivel stud. The rear bag should be further back than in the picture, not touching the pistol grip nor the sling swivel. Grip the rifle with a moderate, you don't have to white knuckle it. Adjust the bags until the crosshairs are centered on your target and squeeze the trigger. Keep you head down and follow thru, don't rush your shot.
Follow these suggestions and I believe you'll see your grouping ability improve. As suggested, practice, practice, practice. Breath control, sight alignment, trigger squeeze and follow thru are the elements to concentrate on here. What I call "trigger time" is the most important part of practice for me, doesn't matter if it is dry firing, shooting rimfires or centerfires the basics apply to all.
