I changed to the new dll, and it's an improvement. Now other programs will also respond to Play/Pause, which is great. However, MusicBee still doesn't respect other programs. When the key is pressed, though other programs will play/pause, so does MusicBee.
There's apparently some way for Windows to detect who currently "owns" media control, here's a screenshot of what I see when both foobar and Spotify are running: the native Windows controller that appears when pressing a media control key, has an "arrow" button. Clicking it switches from displaying the track of foobar to that of Spotify, and also changes Media Play/Pause to control only that specific program:
At the very least, when music is stopped (not paused) MusicBee should ignore Media Play/Pause.
Really appreciate the quick responses, by the way.