Hey djvmind, tight mixes! (so thanks for sharing, I'm listening while working now haha). Unfortunately I don't quite know the answer to your questions yet, since I'm not too familiar yet with using audio on wordpress.com myself.
I tried looking in a few different browsers, but I don't see an option for downloading, even if I go back to older posts. (I'm looking here now: http://djvmind.com/2012/12/ )
It used to show a way to download it on your other posts?
As a workaround, I'm guessing you might be able to link directly to the mp3 file with a text link and say something like "[Click here to download!]"
Looking at the code, I do see something like this:
"<span id="wp-as-2269_1-container" class="wp-as-prepped">
<audio id="wp-as-2269_1" controls="" preload="none" style="background-color:#FFFFFF;width:290px;" src="http://djvmind.files.wordpress.com/2013/05/power-up-soca-part-2-2013.mp3">
<span id="wp-as-2269_1-nope">Download: power-up-soca-part-2-2013.mp3
So it looks like it's there just not showing. I'll look more into it. I feel like I'm probably missing something.