I'm having a similar issue. I want to set up a PAGE with 1 or more players listed on the page for product testimonies.
When I place the code from your above post into the TEXT (not Visual) part of the editor (for a page), the player AND the code display on the webpage. I have a similar problem in the "testimonials" section of WP, too.
I found this player http://wordpress.org/extend/plugins/haiku-minimalist-audio-player/ that inserts a text link or graphical player for audio playback and installed it. (It may or may not be useful for you, you'll have to try it out.)
With the Haiku player I did have an error code come up in Firefox (which is probably a Firefox issue), however, when I viewed my webpage in Safari, its all perfect. So the Haiku player is something minimal that fits my purposes,is not complicated to set up, and should serve my purpose until I need something more complicated.
I hope you might find use for the Haiku player. Good luck to you!