Go to your local guitar repair place (or find out who does the repairs for your local shop and contact the repairman). Most repairmen have a parts box where you can locate odd screws and gears and even single tuners, and see what can be found.
And no, it doesn't have to be a Martin certified repairman, since it's a simple part replacement, and doesn't alter the instrument. Regluing a bridge or refretting, yes, you should worry about the warranty.
And if it's truly vintage, finding the part may be tricky, but probably not.
And have you looked all through the case and on the floor near where you last opened the case?