Are you shooting off of a Bi pod? Sometimes the heavy barreled rifles without the accustock will flex and touch the barrel if you're shooting from a bi pod or have the rifle resting near the tip of the fore end.
I actually just got one of the Choates that you posted a link to last week for a model 110FP in 25-06. It dropped right in and has plenty of barrel clearance. I like the spacers to adjust the length of pull too. I have not had a chance to shoot it yet but it seems like a very sturdy piece and the synthetic material is plenty thick. The style you linked to though heavy, is not nearly as heavy as the super sniper or ultimate varminter models.

As far as improving rifle accuracy, finding the ammo it likes has been the number one factor in my experience. Occasionally you can find a factory load that a rifle really likes but may have to go through a dozen or more different weights styles etc. to find it.
Over the years I have seen a lot of guys barking up the wrong tree dumping significant amounts of cash into a rifle that only needed a decent load. The easiest and least expensive way to improve every rifle you own is with a starter handloading kit. You can buy everything you need in a Lee Anniversary kit and the Lee manual dies powder bullets and primers to start for the price of that Choate stock, and shoot better ammo with premium components and tune it for your rifle. Yeah I know "scary" but very simple rewarding and most definitely conducive to shooting more. It's easy as falling off a log and as long as you follow a good manuals instructions completely safe.
Good luck