Hi Angus,
I've analysed the video you sent, for example at 1:13 where you just started channel #31, there is immediate high pitch sound, with peak at 8471Hz. If compared to sampling rate that channel runs at, this gives 50780Hz / 8471Hz = ~5.9946 which is suspiciously close to 6. That means, there is signal that resonates at every 6 samples. It even increases between 1:12 and 1:13, following a standard ramp-up that every channel begins with:

Or here at ~0:10, there is peak at 6359Hz, which again, when dividing 58780Hz, gives ~7.9855, close to resonating at every 8th sample:

So, what we can conclude is that this originates from codec or before (at input) and it isn't something that happens between the device and the rest of your audio chain.
A device with close to zero latency will inevitably fall into this kind of feedback when played loud. You mentioned that the unwanted noise does not happen immediately, only after you play some of the higher notes - and indeed after you do that, it changes - which is only logical (while in #31 granular or #34 Clouds) as that means there is some pitch shifting of the input signal going on.
Sometimes the buzzing is there from the very beginning. It may depend whether a certain channel clears delay buffer or not (this was intentionally left as is, as it often creates interesting results when you run one channel after another).
What you can do to confirm or rule out the possibility that this is simply an audio feedback / Larsen effect, is to press RST+B4, then the buzzing should decay in a few seconds (or not).
Also, is there any difference when you switch the output between Line level and HP level?
Cheers,
Mario