Sure it would be nice to keep some of the stone, but other than those essential things, there is no savings in keeping the building in that shape and then working around the stone.  Better to pull it apart and salvage what you can, new is generally cheaper than restoration.  And, with a clean building lot you could build it all out of reinforced concrete, stud steal studs on the outside foam it and make it very warm, then put the stone face back on it. Then it would be good for 500 years.