bigrich, you can reload that 6.5 x 55 with 85gr bullets @ 3400f/s, that'll be a lot more effective on dogs than a .22-250 and shoot almost as flat.
The Norma load you are using is about as heavy a bullet as you can get for a 6.5.
Try 100gr ballistic tips as well, you can launch them out of a Swede @ 3200 f/s. Again, flat shooting and a lot better down-range energy than you'll ever get from a .22-250 or .243 win.
With a range of bullet weights, from 85gr through to 160gr, a good range of affordable, quality brass available, and an inherent accuracy that others dream of, the 6.5 x 55 is about as good an "all-rounder" as it gets.