Likely the headspace will be okay or not too far from it.
Thing is, you can measure the EFFECTIVE headspace by looking at the pace between the forward face of the Bolt, when the rifle is completely locked-up, and the rear end of the CARTRIDGE.
In theory, the Cartridge should come to a STOP with the Shoulder against the inside shoulder of the Chamber, and the base of the Casing sticking out to the rear just enough to ALMOST touch the bolt-face. But that is in theory.
In actual fact, if the Cartridge Casing is HELD TO the Bolt-face (for instance by the Extractor), then excess space ahead of the Shoulder DOESN'T MATTER. IF there is space there, the Casing will just BLOW OUT FORWARD, fire-forming the brass to your Chamber. HATCHER has a whole chapter on this in "Hatcher's Notebook" and it is fascinating reading. Several years ago, I needed some almost-perfectlt-straight cases for a project. I didn;t have any and you can't buy them, so I grabbed the old M954 Mauser, went out to the range and ran a box of .308W through her. The cases came out of that somewhat-loose .30-'06 chamber straightened out almost perfectly. It was no trouble at all to open out the tiny remaining inward curve of the brass at the case-mouth.
Note that the M954 is a Brazilian Mauser, reconstructed from a pile of worn-out, scrapped rifles and rebored/rechambered to .30-'06. It is a NINETY-EIGHT Mauser action, the same as your rifle. That old long-claw extractor grabs the case when it pops up out of the Magazine and holds it against the Bolt-face so that no matter what you might be cramming into her, you are relatively SAFE. MAUSER actions of the '92, '93, '94, '95, '96 and '98 types all share this feature. It is part of what makes them among the safest rifles ever built.
Note also that any rifle with the long-claw Extractor should only be fed THROUGH THE MAGAZINE. Load your rounds INTO the Magazine and let the Rifle feed itself. As the Cartridges pop up out of the Magazine, they come against the Cartridge Stop at the TOP of the Bolt-face (when the Bolt is unlocked: right side when the Bolt is locked) and stop there, with the Extractor Claw holding them firmly by their Rims, the Claw itself embedded in the Extractor Groove. No matter what the actual gauged headspace of the rifle, they CAN'T go too far forward because the Extractor is holding them in a SAFE position. THIS is why I could bang off a whole box of.308 through a .30-06 rifle with no problems. I would NOT attempt such a stunt with a LOT of rifles, including a Remington 700, because there WOULD be BIG TROUBLES. But with the Mauser it is safe. Many other rifles share this same characteristic: M-1903 Springfield, P-'13, P-'14, M-1917, Ruger 77, Winchester 54, original Winchester Model 70, Remington Model 30 and others. It s the safest and best system ever developed, but it MUST feed from the Magazine. Tossing a round into the chamber and slamming the bolt shut is fine for SOME rifles, but it will WRECK the Extractor on many others, including yours.
Old girl is looking nice. Glad she has a good home.