Thanks everyone for their thoughts.
A couple more notes on this.
The sidecar is the one from 2009 and I'm informed that we did a lot of machining on that robot with the electronics installed. I opened it up (yes, the warranty is now voided

blew it out a bit and now there's a decent green, not quite as bright as the others, on the DSC.
We did look at running the 5V to the NC connector on the limit switches, but we are low on 3 terminal female terminals so are avoiding that one at this point.
We're going to try another sidecar, with a couple of the switch runs converted to shielded cable grounded at the sidecar, and see what we get for results.