Herman, sounds like you've got a shooter. My loaded prefers Remington 150 trainers too. Except for fgmm 168's. Anything sub moa from a semi automatic battle rifle is outstanding in my opinion. Sounds like you had some sub moa groups already. Best my "loaded" has done was 5/8 and that was just a 3 shot group one time. More often it 3/4 to 1 1/4. This is entirely acceptable to me. My newly acquired NM will shoot more like 1/2 to 1 inch groups consistently.
I put the gas shims on at the recommendation of some of the guys over at the M14 forum and what I did for me is shrink the vertical size of my groups by about 30%. Now Kraig is definitely the guru on these rifles, but it can't hurt anything and it's cheap and easy to do. I would definitely do this before I spent the money on a unitized system.
The only place I put the card stock was on the sides of the receiver with just a little bit folded out over the top edge to the stock. Just used one layer. This really seemed to tighten everything up ; receiver to stock, and trigger group lockup got a lot tighter.
I too agree with shooting the irons. It's much easier to get a good cheek weld and you will be amazed at what you can hit with those irons. By far the best irons I've ever had on a rifle. Can you shoot at 50 yards with irons at your range?
All in all, sounds like you have a beautiful shooter. Enjoy!