I shoot several 22-250's, but all are slower twist barrels (12 twist). Kind of always wanted an eight or nine twist barrel in 22-250, but so far have resisted. The .243 Winchester is OK at best. If your action will handle the 6mm Remington, I'd go that route. Might also look at the 6XC. Nothing but a 22-250 necked up to 6mm, and a very nice round. The 6/250AI round will do 3000fps with a 105 grain Amax, and maybe another 50fps with some seriously hot loads. But it does 3000fps with four grains less powder!
The problem with the .243 is the shape of the case, and not the volume. Neck is far too short for a 6mm bullet. The T.P. is right in the throat, and that leads to a shorter barrel life. Ackley tried a version, and it was a tad better, but still nothing to write home about. The 6/250AI isn't much better, but the 6XC isn't bad. Yet a generic 6mm Remington will have a much longer barrel life, and the longer neck helps you with the 100+ grain bullets.
Looking at long range 22 center fires, I like the Jaybird. Kind of like an improved 22-250 built off a .243 case. A far better design than Jim Carmichel's designs. Here's a round that is built for the 80 grain bullet from the start, and you factor in an eight twist barrel to give you that long range 22 that will perform very well. Cases are formed out of generic .243 brass, and trimmed to 2.00" Kinda like a .243 AI with a 35 degree shoulder, but necked down to .223.
gary