Sorry but your workaround doesn't work for my ipad...
But funnily enough, today i came across a very strange situation and i would like to know if it's just my device or all devices behave in this way, maybe we can find a quick workaround !
While i was doing a call with skype + headphones, i clicked on the button (from the skype app) to redirect audio through the speakers instead of headphones and i could actually hear sound from my ipad speakers !!
I did some further tests during this skype call, so i opened youtube and watching a video and it also worked through the speakers !
...BUT...
When the skype call ended, everything went back to normal !!
I know this is not a workaround, but maybe if we can find a simple application which does the same thing like what the skype application does, then this stupid issue is 'temporarily fixed'.
(note: i'm saying all this because i don't believe that apple will fix this anytime soon)