I've done this very thing prolly 500+ times in my life as Winny M70's are a pet favorite of mine. The stock doesn't give two craps what action sits in it. The only real issue becomes trigger placement and whether or not the tang feature is going to pair up with the action worth a damn. Making that part work takes some skill sets that a lot of folks are not comfortable with.
The best way to pursue this job is to completely start over. You knock the pillars out, scuff everything up with a tree chipper style carbide burr, and fill the stock back up with the same type of filler material used when it was built.
Again, I have those resources on my floor and were happy to help however if I do it were not going to be anywhere close to your budget.
Happy to help and good luck.