I'm out of idea's.
When I have seen black stuff it's usually the paint - eating gloves, grips, or other rubber items.
If your grips appear 'sticky' that could still be the issue.
If the RPS paint you're shooting is out of Taiwan that could be the issue too.
Try switching to a Procaps ball for a couple of washes, something with 'eco-fill', at least you know that is 100% PEG and made in Canada without oil. If you still see the oily stuff change another variable until you isolate the problem.
Remember also, just because something is 'Eclipse' does not mean it is immune to paint disintegration issues.
Once you have eliminated everything else, you'll know it can only be your wife's fault. I will wait for your post in 'Ask Missy' about that...