Even in 22 rifles in the calibers mentioned from the 223 to the AI I agree for anything much over 300 yards the heavy bullets and fast twist are the only way to go. I found out to 400 yards like Ermie said even the 223 is quite capable of good scores and can group, well. I think after that it is pretty susceptible to more influence in any conditions to keep up with the others.
I personally like his suggestion with the 6mm Dasher, it has proven it's worth, has a huge assortment of quality heavy bullets, and is a little more forgiving to beginners.
Just my opinion but the slightly bigger and heavier bullets the 22 or the 6mm offer at a more moderate speed, matter much more than lighter faster bullets do in either with a proper twist barrel for anything over 200 or 300 yards.
I also have found there is a huge advantage for long range accuracy with any caliber in the bolt action over the Encore. I would never spend the money on a custom Encore if I were intending on using it beyond 200 yards competing against bolt actions at any yardage. I have seen many try to equal the bolt actions accuracy with the Encore, but have never seen any succeed.
I spent the money a few years ago on a 22" shillen select match heavy fluted barrel barrel in 6mm PPC with a tuned Stratton action and trigger, on a bedded Stratton forarm, it chot great 3 or 4 out of 5 shot groups. One of the easiest calibers to load for accuracy, but after 30 years shooting bench rest, most with this caliber, I gave up on the Encore and sold it.
In the same breath, I have a 460 in a Select Match gull bull 14" barrel from MGM again in the Encore that I will never part with and does as good as one can expect from this caliber under MOA. I will never again though spend my money on anything for over 300 yards in the Encore, just far better ways to spend your money for those interests.
JMO and only worth what you spent for it!