I think that a burning Coriolis inside the rings would look just as bad as a regular one does, those collisions aren't a pretty sight.
Agreed. (I'm writing this as Cassini is an hour and a half from scuttling.)
Also, how could one justify that a station got there in the first place?
Very definitely. You wouldn't do that, at the station-location decision point, before your first Vogon Constructor fleet sets out to dig the foundations.
So in my view the simplest solution is really to came up with a maths formula to determine whether a station is too close to the plane of a ring or not, and if so move it slightly upwards.
Ah, right. I'm getting a better idea of how the system works, I think. When the ship enters system (while the VFX is going on), the system uses the stored parameters for planet, station, rings, etc to calculate actual locations, orientations, rotation rates, etc? Then the graphics black boxes get on with drawing things. Several of the components of the standard orbital elements are lumped into a quaternion, but others (I guess the phase relations) dumped.
When you say you'd move the station upwards, do you mean northwards w.r.t. to the planet's rotation axis, or outwards from the planet centre? Outwards would work - reducing the debris impact rate. But moving the station "northwards" would be complicated because the orbit is symmetrical about the planet. So if you preserve the momentum vector but move the location 'X' northwards, the resulting orbit would go up north of the eq.plane, then sweep down, pass through the eq.plane (ring plane) and go southwards.
I can't think of an orbital situation on a ringed planet that could avoid the ring plane - that unavoidablity coupled with dynamic friction is why there are
rings. So you do what Cassini did : cross the ring/eq.plane at appreciable angle (reduces time in the firing line for a particular orbital speed) and stay outwards (latterly inwards) of the main ring debris.
Of course, the dynamical friction that pulls debris towards the equatorial plane making it a ring plane will affect the stations. But it's on a centuries-upwards time scale. The debris disc we're constructing around the Earth hasn't had anything like enough time to relax towards the equatorial/ring plane. Yet.