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.
Jeremy