Issue with Bongo and Line6 Relay G10T-II wireless system

I’ve just picked up one of the new Line6 POD Go Wireless pedalboards, and, for the most part, it’s great. 🙂 Loads of great sounds in there waiting to come out. However, I’ve run into a problem with my two Bongos – when they’re used with the Relay wireless dongle, there’s a rather horrible high-mid whine that just won’t go away. It’s fine with a cable, but, since the wireless system is available, I’d like to be able to actually use it with my two favourite basses.

I have several other active basses and they all work fine with it, with no noise. If I plug the bass into a tuner with a cable, then plug the dongle into the tuner output, it’s fine. I’ve also tried using a TR-to-TR cable extender and I’m still hearing the noise.

I’m wondering, is there something in how the output jack is wired, or how the bass is grounded/shielded, that could cause this sort of issue?

Any and all suggestions are welcome. 😀