Best caliber to build off a short action with small shank?

Since you own 308, 7-08, and 243. You might look into the 260 or 260AI as you could probably get away with the same powder and primers. It would just make it simpler. If you do not want to reload then I'd go with a 6.5 Creedmoore. Exceptional accuracy right out of the box from Hornady.
 
You've got just about everything covered. Sold a .22-250? Good for you, I find them somewhat disappointing.

6.5mm, you have a 7-08 and that in my opinion is a better cartridge. And you have a .243 on the smaller end of the scale.

That leaves one area you don't have covered. And an area no one has touched on yet. How about a .257 Roberts?

You have nothing in .257 cal which has always been my favorite. I've been a big fan of the .25-06 for over 36 years now. You want a short action, that's why the Roberts.
 
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