Franco;
Remember that the Remington is a production grade rifle............... More than likely it's the screw holes on the action, OR, the threading of the shank of the rifles barrel, (and/or the action).
You can "FIX" all these problems. Here's how.........
Have a gunsmith weld up the mounting screw holes, and then set up the action in a line-boring fixture. Recut the threads in the action and true the action face to the threads in the action. Then, re-drill the mounting holes for the scope mounts. Get a set of custom bases such as the Warne's. Then, have the gunsmith lathe-turn a barrel blank in your chambering, (cartridge of your choice) and thread the blank on the same lathe.
Then, ream the chamber with the action/barrel still mounted in the lathe.
Then, mount your "high dollar" scope of choice..... It dosen't really matter which, as long as it's over $1,000.00 as you already have over $3,000.00 invested your "Model-7"
(FWIW; My brother wasted several "once in a life-time" biggame tags on his Bushnell "Trophy" scope. After the third one lost zero and cost him a nice elk in Colorado, and a nice 10pt buck and 7rds wasted on 3 does before he figured out it too had a detached reticle...... He finally spent an additional $150 over the original cost of the Bushnell on a Leupold. Three shots; a trophy elk, a trophy mule deer, and a trophy pronghorn antelope, he's decided that the Leupold is the "cheapest" scope you'll ever buy...........)
When you're finished, you'll then be able to put your ~$30 laser bore sighter in the chamber and have it then "approximate" the POI/POA.
Worth it???? Of course not !!!!!!! That's why you have to "live" with the tolerances of "production" grade rifles.
I had/have an Interarms MkX Mauser. It came in .30/06. With Leupold Vari-X II scope on Leupold rings and bases, it wouldn't hit within 1' (feet) of the "bore sighted" spot at 50yds. The iron sights were run all the way to the left with the front sight and right with the rear sight to get it " on the paper" at 25yds.
However, it was the MOST accurate .30/06, or any .30cal I've ever owned (I've had a BUNCH). I replaced the barrel with a custom .338/06 barrel. It hit almost to POI/POA with the initial bore sighting, everything else is the same. However, the gun won't group better than 2moa........... It's all in the barrel. (I still have the original barrel BTW).
Most of the barrel manufacturers will straighten a "crooked" barrel. This results due to variations in the metal in the barrel, and a "jillion" other variables (including stress relief, and warpage during heat-treating after machining). Savage/Stevens has one person in their barrel division that does nothing but check the barrels for "straightness" and "straightens" the "crooked" ones by various means. (bending, heating, ect......).
The Remington M-7 has a very light weight contour barrel. (I have two...... I know.....). As such it will have such "idiosynchrysies". It has a double whammy....... factory "run of the mill" and light-wt contour. Both spell potential trouble. Many gunsmiths make a good living by "blue-printing" factory actions... (read: M700 "custom" rifles with "match grade barrels"). Both my M7's wear "Leupolds" BTW. Both were picked up "used" at about 1/2 the cost of a new one. In fact, all my Leupolds have been "second hand". Only one's had to go back to Leupold and it was my fault for letting it fall 30' out the door of the shooting house............ But I digress.......
Both my M7's have their "foibles". But, I dearly love them as they have numerous attributes that are otherwise only available "together" in custom rifles costing many times more money......
I'll settle for both giving sub-moa accuracy with one or two specific loads.
Just do as most of the others have said...... Just go shoot that thing and be happy !!!!!!!! And toss that laser bore sighter in the gear bag and make a note of where "zero" is when it's installed.... That's all they're good for anyhow.................