Your animation made me laugh with glee when I saw it for the first time !
Well, you do reset the context on scene load, but I assume you are looking to avoid the showSceneNamed call. It does appear that you can replay the audio, but your callback isn't being called correctly. Try adding a
console.log("timelineTime = " + timelineTime); to the else condition in
drawStatic() and you'll see that it isn't being called with the times. You should be able to drive Hype just fine if these values were correct. My guess is that it is some sort of issue in the bufferloader.js code. Of course, you could always reset without reloading the scene, but you'd need to move code around so that was done on the button press.
I'm not sure what is going on here; it appears the audio context is giving a later time that what is really being played. Might be an android/chrome bug.