Thanks!

I have a push-feed Winchester M70, likely made in 1999, in 7mm Remington Magnum. When the bolt's retracted, the edge of the bolt face is some 1/16" in front of the back wall of the magazine. Sometimes it will fail to pick up the first cartridge out of the magazine if it's been pushed all the way to the rear of the box in loading. (Subsequent ones feed fine, as recoil pushes them forward.) Can I fix this by just grinding/filing a bit off the front edge of the bolt stop?

Yes

I'd be more tempted to solder/epoxy a brass shim on the rear wall of the magazine box.