What I'm wondering is whether controls have to be still directly connected to the main PC (ie moonlight is casting the display only), or if moonlight also handles controller communication to the PC.

Assuming its the former, I would imagine using a Bluetooth controller connected to the main PC, which would probably limit the physical range that I could leverage this solution.

EDIT: Rereading your comment, perhaps the remote device can handle controls. I will look into this more later when I can research it better. Thanks for sharing!