With streaming audio there is a number of possible flaws, some are very difficult to solve, even pinpoint.
Most problems are related to the router, or settings in the SqueezeCenter software.
A strong signal from the router is absolutely no guarantee of no dropouts whatsoever, the signal strength can be very low and yet you have perfect audio.
The problem you have is in your electrical system and I suggest you consult an electrician. If you have old or flawed switches for instance this can create spikes on your electrical system. If you are using dimmers this can affect some amplifiers (not Bryston though).
You are also, I think, ecperiencing a ground loop in your system, thats why you dont have a problem when using the rca analogue connections. I would suggest you use Toslink from the Duet to the Bryston as Toslink creates a barrier between grounds. Thats also why we here use a filter on the cable tv outlet to the TV, if we dont the cable ground interferes with home ground and you might get start a fire in your flatscreen.
So try Toslink.
I have never ever experienced any hiccups from the digital out from my Squeezebox to the Bryston, but again, I also use the filter on my cable tv outlet.
What I have experienced though is hiccups in the picture from the cable tv decoder while using analogue sound out from the decoder to the Bryston. With digital out to the Bryston the hiccup moved to the sound (not the picture), but with both digital and analogue connected to the Bryston everything was perfect, so just like what you are experiencing with your Duet.
These hiccups had nothing to do with the wiring in my house though, this must have been from the cable tv provider, and the problem went away again.