There's a slim chance that the tuners are the same pattern as another set of tuners out there, vintage Les Paul style Klusons being the one most likely to use a double set of holes. These are Japan made Gotoh deluxe tuners, a quick check on the net should answer this, but switching to other tuners often means different tuner bushings, or ferrules, and that's when you start getting into a can of worms.
Grovers use a 10mm/3/8" bore, and the screw, at the bottom only, is pretty close to the hole in the headstock, which would mean doweling all existing screw holes, drilling new screw holes, rather involved, and devaluating to the guitar's collector value, as well as ruining the originality.
