You could still "scale" the orbits as a function of their actual distance (say a square root or cube root) in pixels which would maybe position them better (although you may already have done that). That wont account for any eccentricity in their orbits, but might give a better visual representation of their distance from the parent body. Then, as long as the orbital rings are drawn as vectors, you could use vector text along the ring to identify its "real" distance.
The same could be done for the planets using a square root of their radius as an image width/height. And then a set of labels identifying what type of planet it is (I.e. terrestrial, gas giant, and so on) and its "real" radius as it compares to some standard (I.e. 1.25 Earth radii).
Again, you may have already thought about all of this, just tossing it out there as food for thought if it is at all helpful to you reaching the end goal for your map.
Edit: I won't talk about whether your physics are impossible or not. That's just way too much math for my tired old brain.
Edit 2: Also, I think what Bindarusa meant was that all the planets don't have to be on the same solar plane.