Here’s the solution… found right after I made the above post, and having search for 2 hours for an alternative… and it’s simple!
The Podcasting plugin allows you to embed MP3’s into an identical flash player just like that used by the Audio Player plugin. By using the tags:
[podcast]full-path-to-mp3-file[/podcast]
This should not feed the file to iTunes with your regular podcasts if you don’t include the enclosure in your post.
So now I can deactivate the Audio Player plugin.