It's a Remington 783. I have thought about filling the stock mostly full with spray foam ,then putting a thick layer of devcon, JB weld, or some other type of epoxy then drilling that for some kind of pad.
See if anyone makes an AR style adjustable stock. I had to do that for my 10/22 to make it kid friendly. I'll go back to my Hogue overmold in a few years when the kiddos are older. (it was cheaper than buying them a youth rifle or youth stock.)
I cut down an H&S precision stock to be able to use a Anshutz style adjustable butt pad. The stock was hollow at the place I needed to cut it off. I carved a wooden filler that fit pretty good and epoxied it into the hollow portion. It worked out fine.
Check in to Boyd's stocks. They aren't that expensive IMHO. It takes very little to fit it(if anything). Most poly stocks are hollow. It will become flimsy if you cut it. I don't think it's worth it in the long run.
The way I did it for my girl was to cut it a 1/4" longer than was needed and put in a wood block to fit. The better the fit the better the job. Glue the wood block in then sand the stock to the block after the glue sets up. Then install the pad. The one I did turned out good. Not great but good. If I did it again I wold use a peace of hard wood about 1" thick. I used a peace of pine 2x4 that I had on hand. I would also fill the stock with foam to get away from the hollow sound the stock makes when you bump something with it.
I have had luck cutting synthetic stocks by filling the stock with expanding foam, and then cutting it just about 1/8" longer than you want, squaring it up on a belt sander, rough fitting the pad, then epoxying the pad to the foam and stock, and then do the finial fitting of the pad on the stock. Actually I believe any of these suggestions will work, it is just getting past putting that saw to a new stock the first time. If you purchase an after market stock, your take-off stock isn't worth much anyway even if you find someone that needs it. If you screw up modifying the factory stock, then you can go to an after market one. If you are successful in modifying the factory, you have gained some gunsmithing skills and knowledge. Good Luck and post some pictures when you are done.
Mike, you're right about taking a saw to that stock being the hardest part, but it's no good if she can't use it. It sounds like my original plans weren't too far off. What I think I might do is drill a couple of 1/2 in. holes in the wood block that gets epoxied in the stock then spray the foam in through those holes. That way there shouldn't be any voids behind the wood. Thanks to all who replied.