I also had an idea for a "One of a kind" character
TOS = The Vulcan, Spock (The very first)
TNG = The Android, Data
DS9 = The Changeling, Odo. I would also add Dax but Trill are kinda well known
VOY = The Borg, Seven Of Nine. Also the children
ENT = ??
I was inspired by an X-Men comic of all things. In it the Danger Room gains sentience and creates a body for itself and challenges the X-Men to a fight to the death.
So would it be a good idea to have the ship in one episode to gain momentary sentience? This sentience then copies itslef into a mechanical humanoid body. But unlike Data, it looks like a machine, maybe bit of Cylon, maybe bit of Robocop. Also, it would have a dynamic personality like The Doctor but prone to mood swings.
Just throwing in ideas.