Good points... The 85 1.8G is the bargain of the group, excellent lens that is 95% of the 1.4 big brother. I have the 1.4D and it is a very good lens, the 1.4G is better and in some ways, the 1.8G is better still, as in CA is lower. You will not want to shoot wide open because of the shallow DOF but for your task, shooting at 1.8 will be better than 1.4. The Blue Channel noise problem is exactly as Perrone said, sensors struggle with it and it is a miracle of engineering that cameras are as good as they are with the cruddy light we feed them sometimes. All bets are off when the light is not broad spectrum. What helps, in RAW is to use Photoshop and apply selective noise reduction on only the blue channel or more aggressively on the blue channel. A common probem when shooting dim color-filtered scenes is trying to bring the image up to daylight tones. If it is dim and masking detail that naturally occurs with dim light and the human eye, try to recreate the dim illumination in your image in post. The lost detail using more NR will look more natural because we decern less detail at dusk or later levels of light. Cameras like the D3s have gotten a whole generation seeking to use the camera as a nightscope, to get daylight rendering of dim, low detail discernible scenes. It does work sometimes but it is not natural looking from an artistic point of view. Photojournalists however are not looking for art, they are looking for detail that propels the story and that is perfect for them. The metering on your camera will try to brighten the dim scene so shooting in manual or with negative Exposure Compensation will achieve more natural dim night-like scenes. Your camera metering will try to expose to middle grey and the scene the art director has created is much lower tone than that, so either turn off the auto exposure or command it to bias towards the under-exposure side. That will reduce the noise a lot, but also reduce detail while being more realistic captures of the actual scene. If the art director thinks the images are too dark, reply that you are capturing his lighting accurately and realistically.....and praise his wise choice when he brings up the light as a result.
In your current setup, I would use manual exposure, buy or beg a 85 1.8G, zoom with my feet since I would have the flexibility for that comes from rehearsals, expose to the scene and not to the meter's middle grey bias, shoot raw, get close enough to fill the screen with the subjects while being sure not to chop off feet or hands(note to self: take my own advice), use selective noise reduction on the Blue Channel, increase contrast a bit, selectively sharpen only edges or not at all, print small. Use AF-S and turn on the AF Assist light to nail focus in dim light. A better choice for focus assistance would be to use a SB series CLS compatible speed-light, set to Commander mode, so its much better patterned near IR AF assist light is engaged. You will get a flash but it will not contribute to the illumination of the shot since the flash control pulses occur before the shutter opens. Tell the art director that he will not need to freak out if he sees the commander flash, the images will be just as dark and moody as he wants the audience to see. With these steps, the D7000 and 85 1.8G should be able to do all you need. As a side benefit of the faster prime, AF performance in low light will be dramatically better. AF sensing occurs with the lens at its widest aperture and then the camera stops down the aperture to reflect the settings, the instant the shutter opens.
A 85 1.8 will meter and AF using 1.8 no matter what you have the camera exposure set for. That means, with no other changes, the AF will have a LOT more light to work with in poor light than your 55-200, even if both are being shot at f/5.6. That is one reason people see big differences in their images when getting their first fast prime in place of their kit lens. AF just works better(besides the optics....some at widest aperture are not as good as the kit lens wide open, like the old 50 1.8D is poor wide open but one sharp mother when stopped down to f/2.8 or smaller. The wider aperture allows the little 50 1.8D to AF better, even if optically it is not great wide open). With the 85 1.8G, you will notice better color and contrast, better AF and lower noise besides excellent resolving power, better than anything you can likely afford without causing marital discord.
Shooting amateur ballet is harder than top dancers because the extreme precision and grace of the best are easier to predict where a movement will start and end and where the apex will be, consistently within an inch or two. Speed seems to stop, some of the leaps appear that the laws of gravity have been suspended, all of which give the photographer a helping hand. It is almost inhuman, the athleticism and strength they have in reserve to make it look so effortless. With amateurs you know they are working hard, it shows in every move and that translates into inconsistency. When shooting at the Mariinsky, I could set a camera at a pre-focused spot in mid air and have them fill that frame when the expected set is executed with a repeated precision to +/- an inch. And only those within 2 feet could tell the extreme muscle control and power being used to make it look so graceful and light, weightless. I think ballet is one of the most physical of "sports". There has never been a great dancer who was not also a supreme athlete. One of the main elements that hold back most amateurs is lack of conditioning. Few people have the drive and dedication to will themselves into the ultimate movement machines that great, or even good, dancers are. Just training the joints so have extension and power when rotated 90 degrees from normal is a feat that takes years and needs to start young. Most movements in classical ballet start and end with the whole leg, from the hip, "turned-out" 90 degrees from the torso. Good Luck and have fun! Stan St Petersburg Russia