Early run 3650s were notorious for syncrho issues and overfilling caused windage issues. The good news is a rebuilt one is not exactly breaking the bank and they are not very hard to swap out if you can get access to a lift.
I'd try 3.2 quarts of Pennzoil Synchromesh and see what that does. If not... probly a shot syncrho or something else boogered up internally. I just put a rebuilt 3650 in my 98 and it practically falls into gear at 6k. I hear all sorts of 3650 horror stories but when they are updated with all the TSBs, they are great transmissions.
2000 Mustang GT Steeda #0048 34k miles. 99 Cobra 4V swapped, FTBR IRS swapped, exhaust, tuned by James Gordon.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.