The best accuracy improving modification for the 336 is to replace the trigger. The 8 lb factory trigger that feels like two pieces of sand paper rubbing together does nothing to enhance accuracy.
Just keep in mind that replacing the two-piece trigger with a one-piece negates one of the safety/reliability features of the rifle -- sear reset independent of trigger.
You do so at your own risk.
You're better off stoning the hammer and sear, than spending money on a one-piece trigger, only to find out that the hammer was 90% of the problem.
AND, you won't get a lighter pull weight unless you replace the trigger/trigger block spring with a lighter spring.
Lightening that spring, of course, compromises yet another safety feature -- ensuring the trigger can't be pulled with the locking bolt out of battery.
And, should you decide to follow the latest trends and also put a one-piece firing pin in the rifle, you eliminate another safety feature (some people argue that it's two): Another method of ensuring the rifle won't fire with the locking bolt out of battery. (And a 'drop safety' for people that think the spring-loaded rear firing pin works as such.)
Combining those 'by-passed' safety features, without the knowledge to do so properly, is not a recommended practice.
And ... well, if a one-piece firing pin, one-piece trigger, and smoother operation were what you were after... Why didn't you just buy a Winchester, to begin with?