No.

Seriously: This is being brought up time and time again and the devs are aware of this wish. However, they've actually adressed it as being something that is not possible with the way this game handles its audio-files - I cant claim that I understand how or why its not possible because I dont know anything about coding such things, all I know is that its apparently pretty difficult within the code of this game. Does that suck? Yes. Is there a magic wand to just fix the code issues that prevent us from getting such things? Nope. Would it be worth to re-do the whole code and basically build the game from the ground up again? Probably not. So... the last answer here is: Yes, we do have to live with those shortcomings until they find a workaround. If they find a workaround.

Until then, best way to handle it would be to mute the game and turn on your own music in the background instead. Or just mute the music of the game, if you need soundeffects etc. for timing and the like.