If you already have the dies and brass for the .220 Swift it would be easier/cheaper to stay that course. Going to the AI version would only cost you dies and maybe more brass, depending on how shot what you have is. Annealing may bring it back around.
If you want a "new" barrel and really wanted to stay .224 cal then consider the .22-250 AI or .22-243 Middlestead. Both are hotrod .22's. Not sure of the shoulder angle of the Middlestead but the AI version of cartridges makes case stretching not an issue, so I've read. Die setup helps with this issue also.
If you decide .243 cal, then there are a multitude of great 6mm's out there. Personally, I like the idea of owning a .243 AI. Don't overlook the 6-284 or 6-06, both high end 6's.
The 6mm's will have a slight edge in the wind and at extended ranges (over the horizon
). Put all your choices on little pieces of paper, put them in a hat and let your wife choose. This way, down the road if you don't like it that much or want something else, blame it on her. She chose it for you!