brownium

Thanks, Shawn. The audio links in the podcast episodes are done as

[audio mp3="http://songskirmish.com/wp-content/uploads/2017/04/Throw-Me-A-Bone_brownium.mp3"][/audio]

Those links were there long before I installed PowerPress. PowerPress automatically dupilcated those links in it’s own “media url” field when I installed the plug in.

Your answer certainly matches the behaviour that I am seeing, except that both players that I see are the player configured by PowerPress, rather than one player that is the default player, and one that is the PowerPress player.
The question that remains is (and this is just curiosity), what is meant by the following statement on the PowerPress site:

PowerPress logic adds the player and links only once for a given post or page. This is to prevent duplicate players from appearing in a page.

When PowerPress is installed, it hides BOTH players in the edit window of the post, but both show up in the live view. That text above makes it sound like PowerPress should be preventing the WordPress-spawned player in the live view.