I think I finally (as in "FINALLY!!!!") managed to make my game :
1. load completely
2. preload sounds
3. play sounds
on iOS using Safari.
If anyone else is having issues with any of those points and is looking for the right way to make this work now in 2015, here is what worked for me (I could only test on iOS 6 but from what I can see around the forums, many people have had problems similar to mine using more recent versions of iOS as well) :
This will probably mean your game won't have sounds if someone plays it in offline mode. But hey, NOW IT WORKS at least!
Thanks to jeansson who put me on the right track on this thread :
Develop games in your browser. Powerful, performant & highly capable.