You took the transmission completely apart, cleaned, inspected everything, reassembled it with all new soft parts and new or recondition hard parts, put it back in and the above represents your first test drive?
If so, what did you find when you took it apart???
If you properly rebuilt the transmission, you shouldn't have any false neutrals whatsoever nor should you have any downshifting problems. You should especially not have any scraping noises, lol. If you willing/able to explain what you found, post some pics of any damage then walk through what you did upon overhaul (parts replaced, procedures followed, any hard part reconditioning, etc I may be able to help you figure out why you're having the above described symptoms but for now, my response is