Thanks man. Looking nice!. I love this kind of projects to give new life and purpose to an old rifle.
I know how much this rifle means to you as it was your grandpas.
It seems the ruger barrel nut blends pretty well with the winchester although the bluing is a bit out of sync.
you also want to bed that bad boy using a couple of bushings like these...
http://erniethegunsmith.com/catalog/i155.html
Using the no-stress method you could dig a bit more with the dremel and then give some rigidity and bed all
around the recoil lug and skim bed under the barrel. I would actually consider opening up the barrel channel
a tad and reinforce it with a threaded metal rod or something and wrap the barrel around several times with tape
so the channel will take a wider profile if you want to go that way ina a swap later on.
Bart b. also suggested to open that up and I agree so when you bed it that is the perfect time to do it.
I think with some old stocks not only makes them more robust and prevents potential failure but
a tad of rigidity and weight will help with accuracy. From the back of the stock you could drill deep into the grip
and insert another threaded rod with epoxy in case you fall this could prevent the stock from breaking by the grip.
The same channel could be used to later insert a small pvc tube with lead shot in case you want a bit more weight
to counter-balance and also works as a dead blow weight so it helps wiht any recoil.
When you get to 308 and heavy loads like 180gr then the tad extra weight is a welcome addition to help with the
beating. Same thing removing the hard butt plate but that is a sensitive matter as it will alter the original aesthetics a tad.
But some softer modern ones look classic and are better than an old hard one.