You'll get lots of answers...but here I go. It sounds like your screen filter hasn't been screening or filtering for a while! So you want a new screen and new fluid. I would tend to put in the screen after draining the junk in there. Then fill and drain again after running for a bit. Clean the screen and hopelfully you collect some stuff. Then put in your now re-cleaned screen with new fluid (?overkill-get more opinions) I know it is a lot of fluid but it sounds you you could have a tranny case full of b"bits-o-junk" and I would want that stuff outta there pronto.
Peter