^^^This might be the easiest solution--if you can find one.
Have had a T3x 1-8 .22-250 sporter for maybe 3 years now, which at the time came from a special run from Whittaker Guns of Owensboro, Kentucky. My wife has been using it at her pronghorn and deer rifle for a while now, and it works great with 70-grain Hornady GMXs--but also shoots great with lead-core varmint bullets in the 80-85 grain range.
Some have also mentioned Shaw barrels. I have had very good luck with their accuracy since Shaw (then E.R. Shaw) retooled around 20 years ago, and my latest is a 6mm-06 stainless barrel duplicating Remington sporter weight that I had installed on a 700 action in early 2020. Shaw installed it, lapping the lugs and squaring the face of the barrel, and it shoots several loads into 1/2" or less. They charge very affordable prices for their barrels and work--and offer 1-8 twist .224 barrels. (While they offer Remington-contour barrels in 3 different weights, they don't offer Mountain Rifle contours.)
Their standard available chamberings (no extra charge) include the .22-250, .22-250 AI and .22 Creedmoor. The last two are basically the same cartridge. As I pointed out in one of my early articles on the 6.5 Creedmoor that it's essentially the old RCBS wildcat, the 6.5/.250 Savage Improved. (That article was written so long ago that some people were worried about obtaining 6.5 Creedmoor brass if the round "failed commercially." I found it could be fireformed in one step with the Cream of Wheat method with .22-250 brass.)
