While that sounds like it would be a nice implementation, until it comes around, would you consider this temporary solution?

You can go into system configuration, then go to sound settings. At the top, there is an option to make the window still make sounds while the window is inactive. Check this, then uncheck everything except system sounds (which I believe is what that chime for duty pop is under). This way, when your dungeon pops, you will receive a sound prompt at least.^^

I hope this can help you until a taskbar flash alert comes along.