I need help indentifying this Omega Seamaster...

Your mum threw away 2000 watches ?

That isn't "cleaning mode" - that's "I won the lottery but I'm burning all the cash" mode. The best thing may be to get them out of her house and into yours if she doesn't like them cluttering up her place.

If the volume is too much handle, you might want to think about contacting an auction house. They'll be able to appraise and catalogue anything worth selling & deal with the sales. Of course you'll pay them well for it, but you'll still be better off than trying to research and sell each watch independently over the next few years.

Good luck !