Your stated uses are gophers and long range target.
A gun for gophers needs accuracy, cheap ammo or components, and small powder loads to prevent barrel heating.
Long range target needs accuracy, cartridge overall length room in the magazine to load loooong bullets and a fast barrel twist to shoot loooong bullets.
I'd shoot a fast twist factory 223 for gophers and long range target. Having said that, your preference of 22-250 has some merit too, including the ability to load down to 223 (although you'll still need more powder and make more heat than a 223 for a given speed). Driving a long bullet at a higher speed will let you use a slightly slower twist, although I do believe a Rem 223 will be the fastest factory twist available. For long bullets you'll need 1-9 or better yet 1-8 (custom only I think).
You ask about Ackleying it. Sure, fill your boots, but if you are going to, I'd shoot the factory barrel until the throat erodes enough to start causing accuracy problems (or a couple thousand rounds anyway), then set the barrel back one thread and Ackley it, since changing to Ackley needs the barrel set back regardless. After the Ackley throat starts to die, rebarrel in the Kreiger at a twist of your choice.
Regarding a custom, the Stevens might not be the ideal choice. A custom barrel will run you almost twice what a Stevens donor will cost. The stock is going to have to be replaced also or you will waste your investment in the barrel. By the time you lay out $ for a barrel and stock, the difference in cost between a Rem 700 donor and a Stevens donor is quite small compared to the total cost of the rifle.
