I guess it wasn't fully made clear that you have to use parallel, identically-named (down to even the case and spacing of those names) scenes on the controlling and controlled machines for what you're doing. In my case, I need to be able to start streaming, indicate in-band which machine is working to make sure pre-flight that things are working, select the NDI receiver scene, as well as end-of-stream activities.
In my case, the server is the full arbiter of everything that was happening, right down to when to begin and end the stream.
That said, I set something up to I could take full control from the gaming machine from start to finish, running a full test stream, and it worked perfectly.