Great topic, Chris!
Here are some items that I have on hand at the ballet:
While it won't fit in a kit, have a set of crutches on hand, if at all possible. Advil is a must, or the caffeine laced Pain-Aid.
Also, you need to have some training to use it, as we have a staff Physical Therapist who applies it: Kinesio Tape (brand name: Rock Tape). You can get connected to some via rocktape.com
It comes in a variety of colors, so it should be easy to find something that matches the dancer's skin tone, or at least something light enough to not show through tights/leggings. A lot of my dancers are using it lately and it really helps (men & women). Be aware that it can be pricey. We were able to get ours donated. It's worth a shot to ask a local doctor/distributor if they'd be willing to do that for you.
You've listed ice packs: it is helpful to have something to tie the ice pack to the dancer's body. Many of my dancers just use a spare legwarmer, but if you can have a few washable ace wraps on hand, that would be great. And it is generally better to use real ice in a ziploc instead of those instant ice packs or gel packs. (Though they are great to have in case of emergency.) You should not apply the ice pack directly to the skin - so have some scrap muslin or other cheap fabric in your kit, to use as a barrier between the ice and the dancer.
I'd also recommend all of the other basic items you'd carry in a regular SM Medical kit. To pare it down to what my dancers use most: other forms of pain pills, (in case any of your dancers have allergies to Ibuprofen), antacids, eye drops, and cough drops.
And have gloves for yourself and alcohol wipes, as you may be helping clean up blood. Many male dancers, when landing, tend to either bleed from the knee or the top of their feet.
Merde!