Sadly the good Doctor is already 10,000 affection and unlocked in my legacy indicating that all his quests are complete. The only companions that are not unlocked are Kaliyo and Vector. Kaliyo is at 10,000 affection and Vector is up to about 8k as of yesterday. With all the class and planet quests done the only thing left is some linked conversation with Vector but I'm not holding my breath.
Oh and yes, I've been to both a cantina (rest area) and my ship and have no quests and I have nothing but flashpoints and dailies in my quest list.