When chasing an 'at speed vibration', I replaced wheel bearings, had the tires rebalanced etc. so I kept looking. I noticed the same thing on my AOD...seemed to be too much play in the output bushing. Got set up with a shop where they know and own SCs, and took it in.
They had a new output bushing/seal kit ready to go. When I pointed out the same movement, they said it was normal unless the seal was wasted/leaking, took a closer look on their own, etc. No repairs made. Vibration turned out to be a tire wear on the rear and went away with a new set. No issue since.
Since your's is leaking, it might be time for a new output bushing and seal.