The problem can be easily solved in several ways;

1. Use tuning pin tightener, which swells the wood (the best way);

2. Lightly swab the capstan holes with burnt shellac, Krazy Glue
or PVC-e;

3. Steam the rear of the keys (or player fingers);

4. Cross plug the capstan holes with plugs made from identical
material and re-drill;

5. Carefully drill all the way through and use longer grand piano
capstans that will get a deeper grip in the wood, cutting off the
excess threads.

Too bad they do not make oversize capstans!

Andy Taylor