I see.
Well, considering that SEO is irrelevant here and the request to have fluid music is quite unusual and hard to achieve the other way, I would probably stick to the solution you have. I doubt it's possible to have uninterrupted music during the page loading.
The only alternative I see is to have a player started on the index page and then automatically open the actual index page in the new window. This way the player will play the music constantly on the background window while user will browse the site in another one. I have not tried it though. And of course there are disadvantages to this approach.