This one should PROBABLY be in the sports forum. I don't have a D4, but the sensor is essentially the same sensitivity as the D3s, of which I have a pair.
The problem you have is one that faces many people. Unfortunately, there is no easy answer.
On a full sized soccer field, you'll need a 600mm to fill the frame from behind one endline, to the other goal. A 400 will do "ok", but it's going to be a bit short. By the time the play gets to midfield, you'll want a 300. And when play get's closer than that, you need to switch onto the 70-200 as you well know.
In volleyball, unless you are shooting from the bleachers FAR away, the 400 will be much too tight. I use a 300 and my 70-200 in the gym, and I am pleased with that combo. For basketball, a 24-70 is going to be more appropriate for shooting the near court, and the 70-200 or 300 would be better for far court.
Baseball is another problem. Shooting from the first or third base well, you can get nice framing on the batter with the 70-200, but the 300 is nicer for getting out to second base or the opposite bag. For outfield a 400 or 600 is desired.
This is the reason I H*A*T*E that Nikon stopped making pro level DX cameras. Because the additional crop factor let you get away with a bit less lens. You could use the 70-200 where the 300 needs to be on full frame.
I solved this problem for daylight or well lit night games by going with the D800. With the 300 on it, as long as I am not too tight, it lets me crop and keep a lot of information.
Again, there is no easy solution here, and you've got to bite the bullet one way or the other. If it were me, I'd probably get the 300. I say that having made this choice, and going with the 300 BEFORE I moved to full frame. There are a LOT of times I wish I had the 400 and I'll probably get one, but it would be unusable in a lot of situations I shoot because it would be too tight.
The nice thing, is you buy one of these lenses used, and find it's not working for you, you can sell it for about what you paid and get something different. So don't feel like you are going to be stuck if you get the wrong one. 300s and 400s trade hands every week in the sports world. There will ALWAYS be willing buyers.