Thank you so much for that extensive and very valuable response!
BTW, the last (& only time) that I have been in St. Petersburg (1968 or 1969), I had the extreme pleasure and privilege of sitting in the first row at the graduation performance of the Mariinsky! (No camera, of course). Is that the 250 year-old theater to which you refer? 1783 + 250 = 2033: close!
Meanwhile, back in Rockville, MD:
Short of filling in the equipment on my profile, for now: I have ben using only a 35 mm f/1.8 (DX) in the theater. But I also have a 50 mm f/1.8 (FX); my other lens is the 55-200 f/4-5.6 zoom (DX). I am only allowed to shoot at dress rehearsals, but then I have the run of the place (but I never asked to go up to the very shallow balcony at the back of the theater.) And no limit on lens size, either. That means right at the edge of the stage, or often about ten feet back from the front, at the first row. For the full stage, about 30-40 ft back. Wherever I wish. Typically, I am at the right corner of the stage, right up against the front (over the closed orchestra pit), or seated in the front row, about 10 feet back from the front of the stage. Or, to get the whole stage, about 35 feet back, up one aisle.
Shooting RAW, shutter priority at 1/200, manual focus (to avoid hunting in low light), ADR off, high ISO noise control off, auto WB, manually set ISO just above the LO warning. I check the histogram after each shot.
When shooting from the first row, there is a lot of black on the lower 1/4 - 1/3 of the frame: big waste; this is the front wall of the stage. I avoid letting this factor into the ISO setting, but obviously it needs to get cropped out, so it is part of the reach issue.
The lighting is so variable that I can get by with, say, ISO around 1000, or 1600, or 2000, depending on the scene. If possible I do try to stay at 3200 or less. But sometimes, I need the HI range. Perhaps I simply need to rule out action shots when I need more than ISO 3200.
The light is all overhead stage lighting, so I use a lens hood. The director seems not to like using spots. The lighting director argues with the artistic director that the light is insufficient. The lighting director is correct, but loses the argument.
The theater is modern & "small". Perhaps only 40 rows deep. There are no boxes.
As to depth of field, I do not see much issue there, as the focus is either on the featured performer or group, from about 10 feet back, or, if a large group, from 30-40 ft back from the edge of the stage. I say that using the in-focus spot. Perhaps looking at the results would show out-of focus personnel at the back of the stage when I shoot typically from the first row, but I don't see that in the viewfinder. It may show up in crops.
I agree that part (or perhaps most) of the problem is noise showing from blowing up. I had thought of using a zoom, but was concerned about the relative light loss. Perhaps that would be the way to go. Also, the 35 f/1.8 has no VR. I had guessed (apparently wrong) that f/1.8 and a 50% crop was better (from a noise aspect) than f/2.8 and no crop.
Apart from the crop/noise issue (which you suggest could be ameliorated with a longer focal length lens), I have not been familiar enough with the choreography to change shutter speed as the action continues. You have a point that there are moments when the action is slow enough to support a slow shutter speed. But I am still learning about anticipating them, as you refer. (I have experienced that to which you refer.) Meanwhile, I have been looking to capture grands jetees, etc. (Mostly, I shoot sports.) The director is looking for those shots from me.
Your summary of the issues as: reach, concentration on more motion that the light & SS can support is certainly to the point. Because I can locate anywhere, including at the very foot of the stage, reach is not always an issue, although, when the featured performer is at the other side of the stage, it can be. I'll need to look at some shots to see how much of the problem is reach. Recalling the last shoot, i think I typically need to crop to about half the frame much of the time, so, reach would be an issue.
To summarize: solve the reach problem first to avoid cropping (but the 70-200 f/2/8 is about $2400, the new f/4 is $1400). Then, avoid high shutter speed if the lighting won't support it (up to ISO 3200). This appears to come before the issue of moving to a used D3s. Unclear, though, is where in this plot moving to a D600 fits.
I'll pick out some samples.
But how do I post them? I don't see the post option now, but that may be because but I need to renew my paid membership, which recently lapsed. I'll do that now. (Done.)
Your explanation about the Canon vs Nikon sharpness comparison is very enlightening. The other thing I noticed (on DPR) is that with NR OFF, comparing the noise levels among the MKIII, the D7000, and the D600: at 6400, with NR off, the D600 and the MKIII are quite close, and the D7000 is a little (a vague term) noisier. Or is the comparison meaningless?