If you've been struggling with an older factory 250 that won't group, just about any modern varmint cartridge sent through a new barrel sitting in a correctly bedded stock topped with a good optic is going to flip your shooting world from night to day.
I would not mess with an AI or other fire form cartridge at this stage, the performance gains are not worth the effort. 6CM, excellent and you can find ammo and components to feed it. Same for 6BR, .243, .223, and your good old .22-250 that you may already have a stockpile of brass and loading components for. But a 6CM, 250AI, 22CM, etc. are going to burn through barrels in about 1/4 the time a .223 or 6BR will. IMO, there is way too much emphasis (read wasted $$$ and effort) spent on marginal gain cartridges that have way too many negatives and their performance never gets fully exploited.
I should take my own advice though, I have two WSSM's, a .22BR and a 30BR. And I love them all, but I also know when it comes down to it, my hyper-accurate .223's and 6BR's are exceedingly hard to beat, unless the target has hooves....
and +1 on doing a remage (plus 10 on Remage Criterion's)
plus another on buying an inexpensive borescope and getting your eyes opened to how badly an old barrel can be fouled and whether the throat is eroded past the point of no return.