The only experience I have with removing bedding compound from a stock is Ruger M77 25/06Rem that was bedded the entire length of the fore stock. The barrel had a lot of upward pressure from the bedding and to free float the barrel I used a deep-wall socket and very rough sandpaper and removed a lot of bedding compound from the barrel channel to achieve my goal. The bedding can be removed from the stock but will probably require the use of a dremel, because sanding in the recesses will be all but impossible without it. You will only want to remove just enough material so as to leave enough clearance to rebed the barreled action you want to install.
I will probably get flamed for recommending a Dremel to do this job but I don't see any other option, but if there are better ideas for this I will learn from others suggestions.