There was a recent magazine article concerning these, but I can't find it right now. Officiandos include the likes of Terry Wieland and Layne Simpson.
There's three classes of Win. Model 70s: Pre-WWII, post WWII - pre '64, and post '64. The rarest, and thus most desirable and most valuable, are the pre-WWII versions. Because Winchester also launched the .300 H&H Magnum at about the same time as the Model 70, I would suspect that a vintage '38 could have considerable value.
Terry Wieland has a good article in the May 2011 issue of "Rifle", "Restoration: Comedy or Tragedy". One of the first points he makes regarding collectors' value is that condition is everything. a) it must be completely original, including finish, and b) it must be in very good condition. Collectors are not very interested in beat up, battle scarred (some military guns aside) nor even slightly modified, firearms.
From what I've read, the pre-WWII Model 70 is just about the holy grail of collectible American made sporting rifles. Caliber is very significant relative to value, in part because of rarity due to limited production numbers. Prior to WWII the 30.06 completely dominated the sporting rifle market, and thus it is likely that early production numbers of the new to the US market .300 H&H Magnum were somewhat limited. Indeed, the "Super Thirty", as the first incarnation of the .300 H&H was called, was the Brits' answer to the 30.06, and originally it's performance was only marginally better. It was when Winchester introduced the caliber along with the Model 70, it ultimately became known in the US as the .300 H&H Magnum. And the sudden fame of this caliber in the US was the result of a long range competition victory, albeit by literally a hair.
I doubt that there's any issues with loading the .300 H&H to its potential with modern powders for use with this rifle.
I don't think it would be terribly difficult to authenticate the originality of the rifle's components, given the availability of access to experts via the Internet these days. An article I read a couple years back specifically about collectible Winchesters placed a lot of emphasis on precisely this matter, in large part because some of these rifles...in particular pre-WWII Model 70s... are so valuable that forgeries are not uncommon.
First place to look would be forums/websites dedicated specifically to collectible Winchesters. There you should be able to make contact with someone with access to the latest "Blue Book" for approximate values.