Producer82: You are not missing any options, this functionality is too complicated for us to include since we offer 5 different flash player options in PowerPress.
You can achieve what you want by using the WP Audio Player. The 1 Pixel Out Player has their own JavaScript library for managing instances of their player, which handles the only one instance playing at a time functionality you're seeking. You can continue to use PowerPress, just go to the PowerPress Settings page > Appearance tab and disable the player.
I will warn that even though this seems like it could be a major issue, the same problem exists if you have multiple video embeds from video sharing sites such as YouTube. It can also occur with HTML5 audio/video. I personally wouldn't worry too much about this, but the WP Audio Player is there if that's important to you.