I thought that a .250 Savage headspace gage would be correct, but my interchangeablity chart only shows .22-250, .20-250, and 6mm-.250 as interchangeable. Doesn't show .250 Savage at all.
I have had chambers that would not allow the bolt to close on a go gage. If they weren't dangerous game rifles, and would close on new brass, I left them alone. I check chambers with a go gage and if the bolt closes, I put little square pieces of brass shimstock on the bolt face with light grease, to see just how much over the go gage a chamber is. Best I recall, most no-go gages are .004" to .006" over the go gage. I won't let a chamber go over go + .003". The go gage can be very important because a SAAMI std go gage is sized to permit any major factory ammo to be chambered. Be sure and remove any spring-loaded ejector when checking headspace. At best, it will muddy the feel of the gage, and at worst may mask excessive headspace.
If a bolt will close on a no-go gage, don't shoot the rifle. Doesn't matter to me if it's just .001" over. I saw a Rem 700 .270 WSM that blew a stock into 3 pieces, extruded brass, injured the shooter with shrapnel and splinters, and set the bolt locking lugs back with factory ammo. I don't know how much over no-go it was, but I just figure that no-go means exactly that.
If you don't want to mess with the go gage and shims, get both gages. Don't use factory brass or ammo as a standard.
You mentioned checking with live ammo. Don't do it if the firing pin assembly is in the bolt. I can't make myself cycle live ammo in a functional rifle in my house or in my shop, even Model 70's or Mausers, that have 3 position firing pin safeties. My nerves won't take it.
I know I may sound like an old maid, but anything that can develop 65,000 psi and can kill instantly, leaves no room for short-cuts!
Sorry if I sound preachy, but a fine rifle is a tool that should only be dangerous to whatever is in FRONT of it.
Good shooting, Tom