As it turned out, it's quite easy to to put a Flash player on your music site these days. Just get a copy of XSPF Player, write up a playlist, and stick them both on your site.
I've put up the same selections from Theatre of the Perverse that appear on my MySpace page, plus Overtired, and a bunch of live recordings.
XSPF Music Player is Free [1] software, so not only is cheap, but you can modify it if you don't like the defaults. And it uses MP3 as its format, so uploading your songs doesn't require any conversion. The downside is, you don't have a choice about whether your songs will be downloadable, or just streamed. They must be downloadable – it's how XSPF works.
While I'm here, folks may find these instructions useful: How to correctly insert a Flash into XHTML.
| [1] | "As in freedom" |