After I posted a possible solution, I decided to try to get Teamview working on my DAW as described.
It was a simple matter to connect to the DAW from another PC via TV and get the Win-mixer sounds working (just like the OP did).
However when I tried to get Sonar to play thru the win-mixer and soundcard on the DAW PC, I had nothing but problems.
My DAW is an ASUS X99-A with a RealTek 7.1 HD chipset. I tried for quite a while to get the DAW to play thru the RealTek but could not (sample rates/bit depth equal,etc). To Sonar, the Realtek looks like 4 stereo WaveRT outputs. Sonar supports waveRT since Sonar 6 IIRC so not sure why there is an issue.
I do know I had similar problems on my Toshiba laptop with a Conexant audio chipset using waveRT. I had to resort to ASIO4ALL (retch) to get that working properly.
I also remember that with XP (before waveRT), there were no issues whatsoever with Sonar thru a Realtek AC-97 chipset and I could switch back and forth from WDM to ASIO effortlessly.
I think WaveRT is bypassing the WIn mixer similar to ASIO.
I am not sure that there is a generic recipe for remoting the DAW with TV. It seems like
each setup will need a custom solution dependent on OS and audio chipset
I need to look into this more. I still think that if you can get Sonar to play thru the Win mixer, remoting with TV will work.