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Whoa....wait a minute. I don't have an EXIF browser on this computer, but are you saying the nighttime photos were taken on a D4 with a 400 2.8 lens? Why in the world are you limiting yourself to ISO 6,400? The D4 will be fine at ISO 12,800. These have to be very very heavy crops too because of how they are falling apart.
If you have a D4, why are you even shooting the D7000 at night. It simply can't handle the low light. I understand that you are trying to shoot with multiple lenses, but if you want to switch back and forth, do it based on your shooting position -- and keep all your lenses on the D4.
I don't have a D4 (main body is D3s) but there has to be an explanation as to what is going on here. Shoot me a Private Message if you want to discuss settings, gear, etc for baseball.