1. Get some ammo with a proven track record (168 or 175 FGMM, black hills, or M118LR)
2. Check all screws, scope rings, rails, and action screws, make sure they aren't torqued wrong.
3. make sure there is no pressure point on the barrel, make sure it's floating, and also the tang of the action needs to float.
4. make sure the muzzle brake
is tight on the end (i think the LRH model has a brake) i've done this with my old 300 win mag, wasted a whole ladder test of ammo before noticing...
5. put on a scope with a proven track record, sounds like the scope from your 22-250 sounds like a good idea, then to confirm (if this is the problem) put the .308 win scope on the 22-250 and see how it shoots, to rule out compounded issues.
This should fix it, i'm yet to hear of a savage that won't shoot.... keep us updated!