Were it mine, since the value of the stock is already wrecked via the recoil pad I would refinish it to suit me. Might as well plan on freshening the checkering while you're at it too. Worn old checkering juxtaposed to a pretty new fresh finish just makes the whole project look half done.
Bear in mind if it has a factory glossy barrier finish on it, it is undoubtedly lacquer. Winchester stopped varnishing stuff long before that FWT was built - if originality in that regard is a consideration. Again, were it me I would simply strip it and varnish it with multiple coats of gloss varnish rubbed out between coats until grain fill is achieved, and then knock the gloss off and wax it to provide a relatively thin barrier finish not unlike the factory lacquer.
If the condition of the blued steel parts warrants it, perhaps I would be tempted to scrounge up a nice original stock to dress it up for "Sunday go to meeting" and put the redone stock on it for everyday work.
Good options and advice. If it were me, I'd drop it into a Mcmillan hunters compact or hunters edge: Depending on which fill weight the op desires. Here's an old 270 fwt I did just that with:
I also have to ask the op what year his rifle was made. Someone here may have an original stock laying around in the same vintage he needs. The last one I bought was in excellent condition, so you can still find them if you know where to look... As for the OP's rifle, he's right the stock has lost major value. I always say they turned a $400.00 stock into a $150.00 stock when cutting it down. It is what it is now and its fair game for a good recoil pad, refinish and glass bedding as far as I'm concerned. He should end up with a beautiful shooter when done. Keeping in mind if the refinish is done properly. Check out RGK's refinished model 70 here. That is a prime example of how they should look when done right..