Prediction would be by EM modeling (perhaps NEC-based SW). Or by simply asking the OEM.
Reduction - many approaches:
*If you have extra rings, you might be able to use differential transmission on certain signals so that the coupling of concern comes from two different directions and self-cancels.
*Change the impedance to minimize coupling (perhaps less current/more voltage or vice versa).
*Use carrier frequencies that may have higher coupling but can be easily filtered out.
*Provide a post slip-ring network to cancel out the coupling.
*Digitise the data, etc.
*Ensure that you've arranged the rings in optimum order (grounded returns interspersed between the signals).
Unfortunately I can't change the number of rings, the signals that are put across them, and I can't add any circuitry. I can change the layout of the slip ring, so I'll focus my attention on trying to optimise the layout and order of the rings as you suggest in your last point.
Do you have any more information on how to arrange the rings?
As with many high speed interfaces (the 80-conductor IDE cables come to mind), they often put the ground lines in-between the signal lines to reduce coupling.
The next thing would be to put your most susceptible signals furthest from the signals with the highest current. In other words, you'll probably arrange them in order from noisest to quietest. You'll have to analyse this yourself to make your best guess as to the optimum order. In aircraft, it is very common to have categories and bundle and route the signals by 'EMI category'.
Finally, make sure the wiring isn't a larger issue than the slip rings themselves. It woud be easy to blame the slip rings for a cabling problem. The point here is that the cables are probably much longer than the slip rings. It is probably the parallel alignment of the conductors as much as (or even more than) the ring shape that contributes to the coupling.
I can't think of anything else. Standby in case anyone else has anything to add.
Disclaimer - I don't have any hands on with slip rings, but signal coupling is signal coupling. EMI control is simply making bad antennas.
