The Feed http://edreach.us/?feed=podcast is made by podPress and you can configure it at the podPress Feeds section on the Feed/iTunes Settings page of podPress. It is also possible to add (and configure) further Feeds to your blog in this podPress Feeds section.
When I add a podcast to my post, am I NOT supposed to be checking off RSS or ATOM?
Yes, check off the RSS or ATOM checkboxes when you add a an episode to a post.
But these settings have nothing to do with the http://edreach.us/?feed=playlist.xspf . This special playlist contains all episodes which are .mp3 files and added with podPresss regardless of these settings.
How do I unroute my xspf playlist?
It is already done. If you click on this link http://edreach.us/?feed=playlist.xspf then the download of the playlist starts. That is as it should be. In the last days a different thing happened. When I tried open this playlist URL I always ended up with one of the Feedburner Feeds.
I have also noticed that the http://edreach.us/?feed=podcast URL does no longer lead to the Feedburner version of this Feed.
But now that one of the problems is resolved, you should upload the Development Version of podPress and try to resolve the problem with the invisible player. Use the new option at the Player Settings page of podPress to use an alternative method to load the default skin file of the XSPF player. That will most likely make the player visible.
Furthermore I have discovered that you have placed the RSS image and the iTunes:image files in a sub folder of the podPress plugin. That is/was not a good idea. Because if you upgrade the plugin with the automatic upgrade function of WordPress, WP will remove all files and folder which are in the folder of the plugin and unpack the files and sub folders of the new plugin version afterwards. That is probably why these images are currently not available with the URLs you have used in the Feed settings.
It is a better idea to place such custom files in the wp-content/uploads/ folder.