I can't speak for Einstein or Hawking, but the MATH doesn't lie, and the underlying logic is pretty clear on this matter. If we're flying towards each other, we will both look at each other and we will be able to say the same three things: "You're moving towards me, you have more energy than me, and time is moving slower for you."
I think that's backwards. If we're moving toward each other we're both blue
shifted, not red shifted.