Doesn't have to be Jove.
Saturn, Neptune or Uranus would be more likely given big poppa's acceleration due to gravity.
Imagine doing a plane change in an atmosphere that wouldn't be possible in a single pass orbit. The hypersonic is already available in an aerobreaking regime. Why not use it to light a fire and do some serious delta vee.
It might not be worth the bother but has any work been done on the concept of the engine itself or mission profiles?