As of March 2004, OMEGA has added an outstanding feature on their official website.
Their new OMEGA Vintage Information Database allows you to, after a brief registration, look up a lot of details on vintage models.
When Louis Brandt passed away in 1879, he left the company to his two sons Louis-Paul and Cesar, who moved Omega to Bienne in January 1880.
By 1889, Louis Brandt and Fils became the largest producers of watches in Switzerland, with a production rate of of over 100,000 watches per year.
While the initial release of the database is still being filled in with details, the listings are not totally comprehensive.
You can us the "regular" Omega serial number list as the Regina watches are mixed in with the others, but don't expect anything that can be considered accuracy.
What surprises me is that the Omega name/logo on the dial of 4459004 is exacatly the same as your 1288331, and I understood that the style of logo on the case changed over time?
These attempts come off sounding about as bad as trying to describe an exact car model by saying "I have a red Ford from the mid 1970's with a round steering wheel and black tires." Such vague descriptions usually match so many different models and styles that they accomplish nothing.
To get better results from trying to describe your watch to anyone, here are some tips: OMEGA keeps excellent records on all the watches they have made.
Data adapted with permission from “Omega Speedmaster Evolution” by Roman Hartmann.
Data may not be accurate for Limited Edition Speedmasters and Speedmasters with cal. This serial number data item not given in Hartmann’s data but empirically derived from a consensus of users in various internet Omega collector forums.