This sounds like a troll-job, but in case it’s not:
Here’s some of the more common weight loss tactics. A carbon fiber aftermarket stock should lose some weight, maybe get the barrel shortened if it’s a 24”. Don’t know if that action can be fluted, but if so that’s a couple ounces. Replace the barrel with a fluted barrel. Aftermarket titanium bolt handle.
If the rifle has sentimental value I can see fixing it up. If not,… why would you want to sink “an unlimited budget” into a $250 rifle that’s widely regarded as meh?
Edit: I looked it up and these are listed at 6.75 - 7.25 lbs. Not crazy heavy, especially for a 30-06.
I just put together a 6.5lb (includes scope) Win M70 pushfeed in 30-06. It was synthetic stocked standard model which is pretty much the same as the 670 or any other regular M70 in 30-06.
I made the stock, but a Brown Precision pound'r, MPI, McMillan Edge, or similar would work. Barrel was cut to 22", and recontoured to a light #2 profile. Winchester used a fat #3 profile on these. Fluting isn't the way to go. Recontouring and shortening is the better option to save real weight. Or rebarrel with a light contour. I didn't do any machining on the action, but you can shave about 3-4 ounces with some fat cutting on the rear bridge, bottom of the front ring, sides and fluting the bolt. The actions are heavy in general, but can be lightened a bit.
Last thing was a one piece aluminum bottom metal unit from PTG. Standard hinged, not DBM.
Sell it for a profit and put the money into a new rifle that's already lightweight. You'll end up with a better gun for the same amount of money, and I'm a M70 fan.