Do you have a texture reference object to freeze the 3d texture?
Anywayyou have a second problem too and that is that your exceeding the Nyquist limit with your frequency*. You should lower the frequency of your procedural texture by distance from camera. AA contrast wont really help, since your frequency is so insane. And here also a small preview does significantly worse than final size images since the recostruction of the image is better with higher resolution.
What Nyquist limit essentially says is that if your detail frequency is smaller than one sample distance (in other wods 1 pixel which is your initial sample) then the image can not be coherently rebuilt and it leads to aliasing. AA does only lower the sample size but because its adaptive its going to guess wrong. Its actually easier to just ask for a suitable frequency, and then drop frequencies as you go further away.
If you don't want to fight with the technical stuff then just bake it to a texture as its easy to filter right. Thats what many outfits do when they don't want to pay for a TD to actually look at the stuff, its inferior in some ways but easiest to implement.
*the thing is its looking good for still images but this is a sort of a do or die thing, you either get high frequency and aliasing OR you get filrtered stuff and no aliasing. They are tradeoffs, you cant get both at the same time.