overflow hidden can't be added - it breaks various other things, notably the alert counts.
In general, I don't think there's a really good workaround for this. We aren't really fussed about JS off, particularly for mobile resolutions. The split second thing isn't a huge deal either, IMO (it's actually done that way for improved resize performance; the speed could be done more).
May be worth having another look but on the whole XF's nav structure pretty much dictates this (and it wouldn't change unless that structure was completely redone).