OllieJones on "plugin button to insert a shortcode (not a link) from media_upload / library tab"

Working on a plugin.
I'd like to add a button to the library tab of the media_upload page to insert a shortcode. It's an [audio ] shortcode.

This plugin attempts the same thing, but it stopped working a few versions of wp ago.

http://wordpress.org/extend/plugins/audio-player/

This discussion covers how to make something work

http://wordpress.org/support/topic/plugin-audio-player-not-compatible-with-wordpress-34?replies=29

But what works is the insertion of a corrupt hyperlink : you can't say href="[shortcode'" and expect anything to work.

If you know a good way to insert a program-generated shortcode, that would be very helpful.