The term "synthetic stock" is too broad to give you a good answer.
There are stocks that may be a filled injection molded polypropylene.
The problem with those is you can mix epoxy on a polypro work surface ,let it cure hard,then crack it off. Glues and resins don't stick to some plastics. You might as well try to glass bed a teflon stock. I'd suggest not wasting your time.
Some synthetic stocks are composite. They may have a foam core ,a structure of fiberglass,graphite ,kevlar, bonded by epoxy resin. These certainly may be glass bedded and/or free floated.
And.there may be some stocks in between.... molded of a material that epoxy will stick to.
I can't tell you what you have. If you hog out clearance for the glass bed and free float,then discover the epoxy does not bond.your friend will not be happy.
The Bell and Carlson suggestion is not a bad one. There are a number of composite Rem 700 stocks,vary by weight and price.
No disrespect intended,there may be a bedding problem, but the first thing I'd check with a 300 Rem Ultra mag is the shooter.
Try the old standard of loading your friend's rifle for him. Load a dummy round,or just close the bolt on an empty chamber. Recoil anticipation will be obvious at the trigger pull.
That takes a different fix.