I may be off-base here, but isn't the length contraction backward? Things should appear closer as you approach the speed of light, not farther away. And, it should not matter if you move backward or forward to observe that effect, yet it does (try moving backwards).
Also, relativistic motion doesn't appear to affect the movements of the other actors, though it's kind of hard to tell for certain.
With my very limited understanding, my impression is this:
As you move in relativistic speeds, your eye hits more photos, even those going sideways (or backwards), because the photons at an angle are slower than your eye (imagine a car moving fast through the rain, even drops that go in the other direction will hit your windshield).
Therefore, your field of vision grows (you can see things behind you), but only when walking forward.
I haven't read anything about going backwards, but I imagine that your field of vision would shrink, as you are now faster than photons that would previously hit your eye. My guess is that you would only see photons coming directly to you from your front, until you reached the speed of light and went blind (or could see 360 degrees, moving forward).
I think I got it. Lengths will contract, but when you're moving toward something very quickly, the speed of light remaining constant, it will seem farther away. And the reverse is true when you're moving away from it.
It actually helps to just forget about relativity for a moment, and think about the angles light from distant objects will have to take to intercept you. Then it becomes more clear.