Barrel-nut I agree with you up to a point.Shooter technigue does count, proper form is essential.
My first build was a total factory build, mod. 12 action VLP factory barrel, Mako shark stock, with the precision lug. No bedding but it does have pillars factory installed. Head spaced right at 0.002 and always shot with 60 gr. Sierra varmiters set right at 2.221 ALWAYS, and it is boring to shoot. Very seldom over 1/4" at 100 5 shot. Of course my bench set up cost almost as much as the rifle, and the benches are concrete and dead nuts level. Scope is a Mueller 6-25 mounted with Leupold bases and rings and the accu-trigger is set right at 1.5 lbs.. Put a different shooter behind it and the groups will open up(already have done it).
Now on to the OP's question, one thing I did not see mentioned is the fact you have a mod 11 which has a sporter barrel so while shooting shoot 2-3 shots and let cool then try 2 more. You state you reload so here is where the fun begins, you need to find the bullet, powder , length the gun likes period nothing else will matter as far as the rifle matters. Shoot off a good steady rest with a rear bag and learn breath and trigger control and I believe your rifle is capable of doing what you seek to do, maybe not every time but it should do it.
I would give you my load but all rifles are different and what works in mine probably won't work in yours.Don't through your money away until you get yours as good as you can, then have fun changing things one at a time.

P.S. I also have a 20"( bull barrel) law enforcement model that will shoot in the .3's with almost an identical load.