Yeah +1 to the Savage in a caliber with similar bolt face size. You don't even necessarily need a "short action" either. A beater Savage 110 in '06 or .270, or...many of the early short action calibers with the same size bolt face, (.308, .243, 7mm-08(?) were put in long actions as Savage did not make a "short action" until later on in the 110/10 history, sorry, not sure of year.
Beater Savages are relatively common. You can dump the beater barrel, duracoat the rough action (or not) and put on a .260 barrel, w/o a bolt face change.
I think Brownells sells the entire kit to do this, barrel, barrel vise, wrench and head space gauge,....in a variety of calibers.
Not to hijack, but .358 and .338-06 are some other interesting options. I have considered those, as well as that wind slipping .260, but never made the jump.