Might be able to have a transmission shop look at it, or your local boat dealer.
You'll want to start building a list of places to get stuff you'll need. I'd poke around on google, make a few calls. Get the exact model number of the transmission before you call and I'd search google with that, might find some good TT articles that will give you answers or at least the right questions to ask.
Google is better at finding stuff than the tt search engine. Just my opinion.
On the flip side... I wouldn't blindly send it out to a shop assuming it needs to be repaired. Does it spin ? If you spin it for a while I'd that oil change color back to milky? Save the changed oil, inspect for filings with a magnet. I don't know it it has a transmission filter inside, but I'd look at that.
To be clear, it was you milky trany oil comment that made me think and wonder if that would have caused any internal problems to it... I am not a transmission specialist, last time I took one apart, it was a science project in the high school shop.
Also I'm assuming when you do the rebuild, you'll replace the starter/alternator/water pump(impeller), hoses, other seals/gaskets, main seal and other typical rebuild items (lots of articles on this here).
BTW: Welcome to TT !