Well, there is 'absolute' headspace that is measured with go and 'no go' gauges. Then there is what I'd call 'working' headspace, which is really the amount of 'space' around any particular loaded round.
If I didn't have a go gauge, I'd use a loaded round and check your 'working' headspace. All you need is some scotch tape and a loaded round.
The way I headspace a Savage barrel is with the use of the go-gauge and a single thickness of scotch tape. I make sure the go-gauge will chamber freely and the go-gauge with a single thickness of scotch tape will not chamber. Since Scotch tape is around .002" thick, I then know I have set the barrel to have around .001" of headspace. I just stick one thickness on the head of the go-gauge and trim it all around with an xacto knife.
You can do the same thing with a factory round. Make sure it chambers, then add a thickness of tape, if it chambers, add another thickness. if it takes 4 thickness's to stop it from chambering, then you have around .007" headspace.
That is what I would do to understand more clearly what is going on with your rifle.
I had to turn the barrel on my Savage 3200WSM nearly 1/8 of a turn (removed around .006" of extra space) to get it around .001" clearance. I've heard of others that were shipped with very liberal amounts of headspace
, the nice thing about Savages is that they can be easily fixed at home.
Hope this helps and didn't ramble too much.