UpThePole: These are rare - especially in that condition - and thus are hard to evaluate.
They just are seldom seen for sale in that condition.
I have two pre-64 Winchester Model 70 Bull Guns in caliber 300 H&H Magnum.
One is a pre-war low four digit serial number example in 99% condition with original sling - I value it at an easy $4,000.00+.
The other is a new unfired in the crate latter era gun - I value it at $5,000.00'ish.
I wish I could be more help - speaking of more help what is the serial number range?
Good luck in your dealings.
Hold into the wind
VarmintGuy