Wow, well if you want to give it a shot I am super happy to have mobile use a dedicated route / page for login. Warning though, the Ember stuff is like entering another world when you come from a server generated pages background, there is quite a curve getting used to double routers and so on.
It resolves the issue for ios mobile but would still leave some gaps on ios desktop (iPad).
I would recommend giving the modal hack on ios a shot first (always hide body when modals are open on ios) cause it is way easier of a change. Then see if you feel up to the whole dedicated route thing for mobile.