I temporarily resolved the issue by replacing the cable connecting the Y limit switch and the G shield, and not running it through the drag chain. I thought putting a small capacitor on the switch would eliminate the noise, and it did, but the voltage was dropped down to about 4.6 from 4.8, which is apparently enough for the Arduino to read the pin as low. A new cable fixed the issue.
For a more permanent fix, I was intending to get new cable that was longer to wire the steppers, use shielded cable for the limit switches, make the cable coming out of the machine longer, and terminate them with XLR connectors that can mate with connectors coming from the electronics. That would also make upgrading to the X Controller easier. I should probably go ahead a pull both Y steppers through, and connect them on the electronics end.