Seems this thread is a little alive again... it was so long since the post that I didn't bother to update. I ended up mailing the watch to mailinwatchrepair.com, which seemed to be actually certified for omega service and have a parts account, unlike the original place which seems to have blatantly lied to me about that. The new did a great job. They replaced the broken parts with new ones and the watch is running very well. It took a very long time, but I am happy to wait for good work so very happy with the decision to send it there. I'll use them again the next time I need a watch serviced.
As for the other place, I decided that it was not worth my time and energy to try to get my money back from them (I paid in cash), and I certainly did not want to ask that they fix it when it was clear that they did not care to do good work from the beginning (I didn't even mention in my OP that they hands were not lined up correctly). Maybe I learned a couple little lessons - first, paying in cash comes with its risks, and second, doing business with a place that tells you do don't have to pay the tax to them if you pay in cash may be a bit risky to begin with, haha. I did notice just now that they have removed the "certified Omega service" from their website.
Anyway, onward!!
And as always, thanks to everyone for the advice.