I believe digging the old hinge out would be the right way to repair this. If he works slowly, there shouldn't be too much damage to the wood. Gluing the new hinge in the same place as the old one might inhibit the flexing. CA hinges don't like sharp edges and stiff/too much glue. It might be possible to cut all the old hinges apart and glue new ones right next to the old ones.

Dr.1