I took it to pretty good independent shop. They do not work on transmissions themselves, but at least they confirmed my guess that the noise is coming from transmission. They also called transmission shop that they usually work with. So the next thing they say is to figure out exactly what is wrong with it and how much it is going to cost to rebuild, but they will have to remove and take it apart.
Here is why I think replacing it with used one will be more cost effective than rebuilding it. I hear that street price for such transmission is around $700. That could be a little off since I just could not find exactly the same transmission on either ebay or craigslist. But the transmission shop quoted something $2500 to rebuild and $3100 for factory remanufactured one. Given that price difference I would rather spend a little more and factory rebuilt one.
But if you compare even $2500 to $700 it make a lot of sense getting used one. Of course there is also a risk of getting totally screwed up piece if garbage, but I hope that if person is known here on forums his reputation will be my warranty.
So I guess it is also possible that the local transmission shop is charging too much or that it may not be a really good shop so I wonder. Do you guys know any transmission shop on Internet that is very good?