The common theme is that it is (was) a current FLAT BOTTOMED ACTION and the OP wanted ideas how to bed his flat bottomed action. 40 years ago, using bedding blocks was not quite "in vogue" and the OP has more options today than ever.
Looks like Winchester learned this lesson themselves: America Outdoors - The Aluminum Revolution
To see what we mean, you need look no further than a class of affordable heavy-barreled bolt actions, such as the $705 Remington Model 700VS Varmint Synthetic and Winchester's Model 70 Synthetic Heavy Varmint, $764, to find more sub-inch guns. Recent testing we conducted with these models in .223 Remington found they shot half-inch 100-yard five-shot average groups with at least one ammo brand.
Not surprisingly, the Winchester Model 70 Synthetic Heavy Varmint included pillar bedding and a full-length aluminum block, machine-cut to fit the receiver, and built into the composite stock. Winchester calls this the Pillar Plus Accu Block bedding system, and it includes glass bedding around the front and rear stock screw area of the receiver.
A satin stainless-steel finish on the gun's 26-inch free-floated barrel contrasted nicely with the blued receiver. A 0.87-inch-thick muzzle diameter accounted for much of the gun's 10-pound, 4-ounce weight. At the range, our best five-shot group average (five total groups) with this gun came with PMC's 55-grain hollow-point boattail bullet: 0.38 inches.