I wouldn't recommend opening your 360, unless you can do it without ripping the stickers and other things that Microsoft can tell you opened it. But thats just in case you get the red rings or for some reason you need to send it away. Otherwise it's like 150$ to get it fixed..no matter how minor or major the problem is >_>
And I think you used to be able to do that, but it got fixed by dashboard update a long time ago, (that was playing flash games on 360, but I guess they just blocked all that stuff out aswell) Too lazy to get a full save by yourself ?