I have done my fair share of stage photography and have discovered, the hard way, what the main issue is: overall contrast and local contrast.
At first sight, stage photography appears to be a very high contrast subject, deep shadows and intense highlights. However, it is a low-contrast subject, or rather, two low contrast subjects cramped into the same negative. As stage lighting and photographic lighting techniques are totally different, you have to consider both the illuminated areas (lit faces, for instance) and the shadow areas are two low contrast subjects, each with its own limited luminance range, but yet positioned to the point of being right there at the extremes of the H&D curve even if a compromise exposure is decided upon.
Further compounding the issue is that, while we are hoping to get high film speeds by basically over-developing the under-exposed film, overall contrast might shoot up to the point that the highlights might get blocked up while the shadow densities still cannot build up sufficiently due to the lack of exposure. After all, the "pushing" of film does not appreciably alter the real film speed as measures at the toe of the H&D curve, but rather an equivalent midtone, which, in this case, is sadly lacking.
After much trials and false starts, I have come to use a standardized combination: an inherently fast film, yet one with low base-fog, and give it a speed-increasing compensating development. My combination is Fuji Neopan 1600, rated at 1600 (preferably 800 if possible), exposed for shadow and developed in Tetenal Emofin. Full shadow exposure along with two-bath development brings out extra density and local contrast, but it two-bath development also minimizes the chance for th highlights from blocking up. The resultant negatives invatiably prints easily on standard grade paper with no need for holding back the highlights at all; straight prints all the way.
As usual, YMMV.