Try Nancy Fratti:

  Nancy Fratti Music Boxes
  P.O. Box 400, Canastota, NY 13032-0400 USA
  tel.: 1-315-684-9977  (Mon-Fri. 10am-7pm; Sat. by chance; closed Sun.)
  E-mail:  musicbox@dreamscape.com
  www.nancyfrattimusicboxes.com

I know that Nancy stocks (or can have available) damper rails for the
15-1/2" music box (new replacements); she also has great stores of old
parts for reuse.

Best regards,
Eliyahu Shahar