GR/Hawking Radiation Contradiction

[abomination]

A thought experiment:
Say that you and I decide we are going to go into orbit around a black hole. I am brave and you are weak, so I decide I'm going to take the plunge and you just stay in orbit. As I fall toward the black hole, the strength of the gravitational field increases, and time for me slows down relative to you. So I see your orbiting speed increase. Meanwhile, you are orbiting the black hole, and see the Hawking's Radiation slowly decreasing its mass. You count the number of times you orbit the black hole before it loses so much mass that you escape the orbit: say it's 100 billion times. However, I am observing you from right next to the black hole, and for me Hawking Radiation is happening just as slowly as it is for you. At some point your speed gets so large and time goes on long enough that I see you orbit the black hole 100 billion times. However, the black hole's mass has not decreased that much (since for me it has only been a little while for you to orbit that long, so Hawking Radiation has done little), and so you continue to orbit after the 100 billion orbits.
So, at the end there are two yous: from your point of view you leave orbit after 100 billion orbit, and from my point of view you continue orbiting long after that.
How is this resolved? I asked my professor and he had no idea.

 

[PAllen]

Hopefully this won't hijack the thread, but I have somewhat related mystery about Hawking radiation that I haven't found a solution for. That is, for a spherical, non-rotating, black hole, for sure, an outside observer never observed matter or energy reaching the event horizon (ever so close, but never reaching, let alone crossing). At what point does the outside observer start to see Hawking radiation? Especially, as 'vernacular' derivations involve virtual photons crossing the horizon; but nothing ever crosses according the the outside observer.