I disabled HDMI device control on my TV as well, so I can turn off the TV without it causing the Steam Link to turn off. So, in my case, I have to configure my headset as the Default Device for all sound, then connect the Steam Link to the PC for streaming, and then move Default Device back to my speakers. Then, regardless of changes to the Default Device while streaming, it will continue to capture from that device until streaming is stopped. Moreover, it enumerates the interfaces only when you connect to the host PC, and captures audio from whatever device is the Default Device at that time.
Steam Link will only capture audio from the audio interface marked as the Default Device. I played around, setting different interfaces as the Default Device in windows until one of them worked. In my case, Steam Link just can't seem to stream audio from the audio interface that outputs to my speakers. I just found a solution to my problem as well.