Neat rifle.

The action may be a National Match 1903. That's just a guess from the headless firing pin/cocking piece in the bolt.
Some of the NM were made or could be ordered that way.

Springfield Research Service (.com) will for a fee research the rifle by ser# and if on record verify what it left the S/A as.
A National Match rifle as a starting base rifle would add to the value IMO.

I notice that either G&H or perhaps sometime after that, the rear recv'r ring 'hump' was removed from the action.

That feature is a simple reinforcement over the tunnel that allows the bolt safety lug to clear when working the bolt .
The normal Lyman 48 aperture sights and other brands that are expressly made for the 03 Springfield have a step in the top cross bar of the sight to make it over that hump.
That places the aperture a bit higher and correspondingly it requires a higher front sight to balance that and bring the impact point back down.

I suspect it may have been done when the 'scope mounting was done. It's removal may have given the scope a bit more room to fit coming over that rear ring of the recv'r.
Maybe they just wanted to use a lower rear aperture sight assembly.

All just speculation of course.

I think the stock on it now is not a G&H product just looking at the pics. But just my opinion of course. Checkering pattern and quality doesn't appear to be G&H's nor does the over all stock work. Grip cap isn't what I'd expect to see on a G&H.
But it sure is a great piece of lumber,,and never say never when dealing with these things. Customers had their say as to styles and accessorys. Checkering may simply have been recut somewhere along the way and not done up to G&H standards.
Again just a guess.

Nice find. I hope they can come up with something about it's history for you.

added: That style of Damascene (sp?) on the bolt was very common on the G&H, Hoffman, Hart and others of that period.
The tightly patterned swirl done with an abrasive stick or brush was not as much used as it was later in the 60's and forward.