All these Omega's shared the same balance complete. This is from the Jules Borel website: You will probably end up having to buy the balance complete. Jules Borel doesn't have the part (balance complete or hairspring) in stock.
721/478 (discontinued)
BALANCE COMPLETE, INC
OME 28.10RA
OME 28.10RASC AUTOMATIC SWEEP SECOND
OME 30.10RA AUTOMATIC-INCABLOC
OME 330 AUTO/INCA/FOR 1.07MM HUB STEM USE MOD 28.10R
OME 331 AUTOMATIC-INCABLOC
OME 332 AUTOMATIC SMALL SECOND
OME 333 AUTOMATIC-INCABLOC-REGULATING DEVICE
OME 340 AUTOMATIC-INCABLOC
OME 341 AUTOMATIC-INCABLOC
OME 342 IUTOMATIC-INCABLOC SMALL SECOND
OME 343 AUTOMATIC-INCABLOC-REGULATING DEVICE
OME 344 AUTO**(CUST MUST ALTER SUB BEARING PLATE)** SMALL SECOND
OME 350 AUTOMATIC-SWEEP SECOND-INCABLOC
OME 351 AUTOMATIC-SWEEP-SECOND
OME 352 AUTOMATIC-SWEEP SECOND-INCA-REGULATING DEVICE
OME 353 AUTOMATIC-SWEEP SECOND-CALENDAR
OME 354 AUTOMATIC SWEEP SECOND-INCA
OME 355 INCABLOC
You may want to try one of these companies: McCaw's, Esslingers, Eckcells, and Cas-ker.
If they don't have the part you could also try:
Mechanical Watch Supply LLC: http://mechanicalwatchsupply.com/ Look elsewhere 1st, because he admits he charges more, but he has rare and hard to find wrist and pocket watch parts. rd@mechanicalwatchsupply.com
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Twin City or Barton and Chase may also have the parts you need.