Peppy should just make it easier for us and let ut borrow the multi-spec client. -.-"
Anyways, for the sound problem, I might recommend "VAC" or "Virtual Audio Cable". c: It's not free, but there are sites out there that let you download it. It's just as the name suggests, it's a program the routes the audio from specific programs to locations of your desire. For example you can "add" custom sound-cards that you can set OBS/XSplit to use as an audio source. I'm sure some of you has heard of this before, just felt like mentioning it. Anyhow, this program requires the source of the audio to be able to route to a specific location, like Skype where you can select an outout-device. This doesn't work with osu! though, I think. At least I haven't found any way to do so.
For spectating, can't one person spectate two persons using the osu!test client as well? Or are the live and test clients unable to run at the same time?
One more thing. Boat, I love the idea of using a web-page to "spectate" the players. As mentioned before the players won't be synced though.
Also, I can try to make an overlay for the stream if need be, or if no one else want to.
Edit: Added more content and formatting the text.
Edit: Grammar..