Is it possible for you to use more flashes/strobes with RF triggers and battery packs in this venue? If so, would you be able to set them up around the auditorium before the event? Have been to events in the past where the photographer(s) have placed a half dozen or more flashes to create additional light. Have also seen a couple of places upgrade their lighting after many years of complaints from photographers, teams, parents, and other interested parties. Some of them had banned flash usage and users of the facilities could no longer find photographers willing to work inside them. Nobody wants to buy blurry or grainy photos apparently.

With the extra flashes the shadow lines will be softened. Red eye problems should pretty much disappear. Biggest problem will likely be complaints about all of the flashes going off. This is what led to flash units being banned in above mentioned facilities.

Is it possible for you to use wider aperture lenses? Is it feasible to upgrade your body for better ISO performance? 1D4 1Dx possibly 5D3, are ones that spring to mind depending on what you specifically need. You will lose the 1.6 crop factor, but would gain a lot of ISO headroom.

Poor lighting in some facilities can really make it tough to capture great images. To make it work you either need to create your own light, or find the right combination of lens and body to allow working in the space. When you can't do either, it might be time to spectate.