I built a .22-250 AI as a stunt. Used a 24" Pac-Nor 1:9" twist barrel with the Rem Nut (allows swap barrel with a Savage wrench) and muzzle brake on a new 700 action that was modified to my specifications (double sleeved bolt, bushed firing pin, pinned .250" recoil lug, fitted lugs, Jewel trigger, etc). Solved the fire forming problem with a custom Hornady Hydraulic Forming Die. The die was made to match my chamber reamer drawing and three fired cases. Also had a custom FL die set matched up at the same time. Brass formed in the Hydraulic Forming Die shoots exactly the same as fireformed brass, needs no special loading techniques as headspace is correct right out of the die. One advantage of the Rem Nut is that if the headspace was a tad loose, it could be reset to match by adjusting the barrel, eliminating any fiddling with the dies, however it functioned fine set to the standard GO gauge.
Rifle was built to use lead free bullets, especially 50 grain Barnes Varmint Grenades, with Varget and H-380 it will hold less than .5" for ten shot groups at 100 yards, velocity at 3,737 fps and explosive terminal performance. Seating depth most important accuracy factor with Varmint Grenades, which need long jump. Because of location I use lead free bullets from Barnes and Nosler exclusively. I have found these bullets generally to be as or slightly more accurate than lead core bullets, so there is no need to experiment beyond using them.
Muzzle brake allows me to see impact on ground squirrels. First outing was extremely satisfying as there were no misses, only flying squirrel anatomy and visible shock waves.
I wouldn't do the build again, the .22-250 AI, or even the standard cartridge, offers no advantage over the .204 Ruger or the .223 Remington for the majority of my varmint hunting. When the need is for 300 yard + shooting, I use a custom .243 WSSM on a Savage Target Action with a 26" 1:8" Brux barrel, using 62 grain Varmint Grenades it is more accurate than the various 224's and is so explosive that squirrels stuffed on wet alfalfa vanish - I mean vanish, not even a blood smear, the ground they were on appears to have been rototilled by bullet and squirrel fragments. Even slightly low misses at long range with either .224 or .243 Varmint Grenades will kill squirrels as the explosive bullet fragmentation sends enough shrapnel through them to do the job. One was partially decapitated by splinters from a near miss with the .243 WSSM on a oak tree root at a little over 200 yards, where the bullet passed along the bark underneath his neck (see photos below).