Open Broadcaster Software - Media Playback Solution

Open Broadcaster Software (OBS) is a boon for would-be webcasters on a tight (or zero) budget.
However, OBS does not have a dedicated Media Player feature like Wirecast and other commercial webcast production software packages. Therefore, the monitor capture facility must be used to stream a media player window.
Capturing a running media player window as a cropped part of the overall administration screen can lead to unpredictable results, as the window position can easily be disturbed, and other windows can easily intrude into the selected area. So the option of running the player in a second monitor, and capturing the entire secondary monitor with OBS is an attractive solution.
The dual-monitor approach is demonstrated here, along with an alternative audio routing scheme.