Ok guys, I really did need this functionality so I searched through the plugin database to find something similar.
The people-lists plugin had a (working) bio editor, but I didn't need the rest of it's functionality, so I've isolated the bits needed and created a separate plugin with the functionality I (we) want plus some additional code to bring the end result in line with the expected behavior for the Rich Text Biography plugin.
Tested & found working as desired in WP 3.2.1.
If you're interested, you can download it.
If you do, I'd very much appreciate it if you post back with your test results, i.e. in which WP version did you test it ? and did it work as expected ? if not, what did you do, what was the result and what was the result you expected ?
I'm contacting the authors of the people-lists plugin to see about maintenance and also the author of the rich-text-biography plugin to see about a possible upgrade path for current users.