I think the reason behind not wanting to open new windows is that it destroys the 'Back' arrow so that you might lose people from the site or navigation could become confused. But in the case of yours I can't see the problem.

Another option

You could host the mp3s elsewhere and then embed a player onto your page. On the plus side you'd chop down on your bandwidth as the files would be hosted off site; the page would load up with very little additional time; the viewer would be able to browse the words etc at the same time as it wouldn't launch anything else; it's free. On the possible neagtive side is that there would be some amount of promotional content on the player possibly; there might be some issues uploading the mp3s if it suspects they are copyright (as I would guess many are even though I'm sure they are used with permission); limited ability to change the look.

I very quickly fiddled a bit with one of your pages as an EXAMPLE if you download it you'll get the idea. Your graphics don't show obviously and the link is to another tune but will give the idea. It may well be too obtrusive.

I use esnips because it's free and offers 5gb of space but there are no doubt lots of other similar things.