I would wire both right off the plug to the HU, it probably doesn't really matter, but that's what I would do. I am skeptical that any of this will matter as I can hear differences in the static based on what's running for apps in the HU(High CPU more weird sounds). What is odd is that it doesn't increase with the volume, which would imply something being introduced post-DAC,, post-AMP which would make me think maybe Ferrite on the 4chan would be best bet, but again it's probably too late. I suspect it's internal interference inside the box post-DAC./AMP
I hope you find the solution, but I suspect only way to solve is to run spdif to a DAC or DSP/AMP, which if you don't have the HK system, would be a pretty good Add to the car. With my HK i'm pretty sure I'd spend a bunch of money to get spdif->RCA->Spkr Level to get to the HK AMP and probable end up with some really messed up sound quality. In my corvette it just wouldnt be worth it as I always drive with the top down and at highway speeds I mostly just care about loud! ;-)