I realised that the div movement might work in some browsers, and in others not (work in Chrome, but not in Safari for example).

So, you can play with the z-index in the JS function that triggers the video play (playVideoInJWPlayer). Then listen to the close event of the player (it surely has an API as far as I remeber) and restore the z-index to the state it was before play:

document.getElementById("jwPlayer").style.zIndex = "90";