I'm also interested in linking recordings of my work with the written versions. The main option I can see (not that I've made much use of it yet) is to make the recording available to play somewhere else (I chose SoundCloud) and then just link to that page. I agree that it would be much better to have the written piece and a "play" button right here on deviantART. Still, my method doesn't involve downloading anything (which is a hassle), and doesn't require two versions of your work on deviantART itself.
If you find a more elegant solution, I would be very happy to hear it. #Elocutionists might be worth a look, by the way, if you're not already familiar with the group: they deal with recordings of work, though I haven't really had any experience with them myself yet.