Nice attention to detail in this. By the way, it seems like the new view's shadow in the original actually loses opacity as that view leaves the screen. Did you look around for the blur effect at all? You mentioned it but any luck beyond that? I've seen some attempts but nothing useful.
Yeah, the iOS 7 'frosted glass translucency is impossible to achieve with CSS. Everyone points to filter: blur(), but that only blurs the element, and not items behind it.
The only thing I could come up with was using something like HTML2Canvas[1] to render a portion of the DOM in a canvas/image, position that exactly on top, and then blur that. But all that seems quite convoluted and heavy, so decided not to invest any energy into it.