(this is not an expert opinion so you will have to decide for yourself if the logic is sound)
We discussed some ideas like that as a more efficient way to gather some gasses in LEO than launching it.
The key was that electric thrust is much more efficient in terms of propellent required, but delivers much too low thrust to normally be used to get any mass off a planet.
Because in this case you could build up momentum over time, or only go deep enough to encounter a very slight drag, iondrives and similar high efficiency low thrust methods could be used.
In your case, perhaps you could exploit some sort of slingshotting maneuver between say jupiter and Io, thus not require any energy for thrust at all?
This is my scheme: You approach IO with (momentarily) zero velocity with respect to jupiter. Or to put it another way, You are stationary and Io approaches you. You slingshot around Io, and gain double its velocity. You expend this energy dipping into Jupiter's atmosphere, leaving just enough velocity to intersect your orbit with IO's again, and again restore your velocity to double Io's.
It probably wouldnt actually be zero velocity, I dont think drag from jupiters atmosphere could put you in exactly that position and also I dont know if Io has enough gravity to slingshot you around at that velocity. However you have a whole range of velocities to chose from. So long as your velocity is X less than that of Io when you encounter it, and not so different that Io's gravity is too weak to totally reverse your course, then you can gain Io's velocity + X and expend a velocity of 2X gathering fuel as you dip into jupiter's atmosphere.
What is more, this method gains efficiency the more fuel you gather.
When you finally want to deliver this fuel to a world higher up the well, you could perhaps only slingshot halfway around io and end up heading straight out. You time this maneuver to intersect with another moon and slingshot around it to gain extra energy to propel you higher up the well and so on.
This would probably give you very limited windows in which you can leave, providing useful plot points.