Re: Savage 111 rebarrel
260!!!
Built my first 260 on a long Savage 110 with 'staggerfeed' (attached to action) magazine which came originally as a 270. The 260 loaded and fed perfectly in the magazine. With the target gun having an accutrigger, I'd bet its a newer round back action with a 'centerfeed' (fixed in stock) magazine.
I too found the 30-06 to be "too much gun" for anything other than hunting, but can shoot my 260 all day long without so much as discomfort in my shoulder.
Get a Criterion barrel, Go/No-Go Gage, barrel nut wrench and rock on...
Of course, 243 is a good choice too...