What I normally do on some of my rifles is get either an HS stock or McMillan stock, then have it glass bedded and pillar bedded, and finally have a trigger job on it with pull anywhere from 2.5 lbs to 3.5 pounds depending on cartridge and use.
On my Winchester Classic Stainless in .375H&H Mag, I had all of the above work done, plus I also had the action jewelled, which is really nothing more than just polishing the action to make is silky smooth, and it is - even more so than my Tikkas - AND THAT'S SMOOTH!. Anyway, I forgot how much all that work cost, but it was worth it because I can shoot 3 shot groups at 100 yards of UNDER 1/4"!!! That's right, and that's with plain jane factory Federal 300 grain Hi-Shock round nose ammo. Oddly enough, with the 300 Nosler Partitions, the groups open a bit, but still well below 1MOA. Can you imagine a .375H&H African big game animal rifle that can shoot better than a varmint rifle?!?!?!? Well, I got it. (Keep in mind, however, that since the recoil is so bad, my flinching starts to cause my groups to open up.)
Bottom line is that there is no guarantee that the above work will give you similar results, but there is little doubt that it will definately help to some degree.
BTW, I too absolutely HATE the plastic factory stocks from Remchester.