Would you consider going with a smaller case?
I built a shorterned 243AI to headspace off a 22/250 case. Pretty much an 6XC with a bit more powder capacity because of the sharper shoulder and reduced body taper. Worked quite well. The reamer was not a perfect fit to the dies I wanted to use but the design showed promise.
The issue with the 243AI is the amount of powder you will burn. Barrel wear is going to be brisk. Also, depending on the twist, the bullets may not like going as fast as the 243AI can push it.
There have been a few variants that seem to be doing very well for the owners. 6mmBR.com in their 6mm forum. Was a 243AI with a longer neck and pushed DOWN shoulder to reduce case capacity slightly.
The designer claimed very high bore life using H1000. Haven't kept up with the thread for some time but worth checking out and gaining some insight.
Should be a lot of fun. Enjoy...
Jerry