Is using a fast prime a workable compromise? Yes, but it is a compromise.
I shoot with Nikkor's 50mm f/1.4 for much of my low light imagery, something I really enjoy shooting. However, for sports I would only use it for features. In other words, for stuff I'm real close to that helps build the story. The obligatory coach-talks-to-team shot or the little brother/sister mimics older brother/sister's sports shot or the guy-wearing-ridiculous-beer-helmet-at-highschool-basketball-game shot.
The reason is this...though f/1.4 can look gorgeous and tremendously increases the amount of light your camera can capture, at 50mm the compression just isn't there. A lens that fast will give you great depth of field, which we all love, but your subjects simply will not pop the way they will with a monster 300mm, 400mm or the often coveted 600mm. You can crop in post all you want, but you won't get that delicious stacked feel you get with long glass.
Another thing to consider is the DOF at f/1.4. When your subjects are moving that fast, especially in figure skating when they are coming or going from the camera quickly, your chance of finding solid focus is minimal. You'll blow most or your shots, and you WILL blow the ones you really want. You will think, "Oh, that's the one! But it's out of focus! Darn!"
The best way to maximize light is to introduce light. May not be possible in these venues to use a strobe. I imagine TKD is not the place to be throwing flashes all over. Figure skating maybe, I would ask. If you want tips on mounting strobes and where to place them, let me know.
One more thing, from your statement, "But if I have to stop it down for sharpness, then I lose shutter speed, or have to bump ISO, which is not going to help get better action shots." This is wrong. You want to bump ISO. You want to be shooting at the fastest possible ISO you can, without sacrificing quality of course. From what I understand the D90 handles ISO fairly well. If you can push it to 1250 or 1600, without insane amounts of noise, you'll be able to shoot with a nice f/5.6 200mm. You'll have your light, you'll have your fast shutter, you'll have workable DOF AND you'll have gorgeous compression.
When I shoot highschool football, I shoot at ISO 1250, underexpose 2/3 stops, deal with any noise in post and have always been happy. I get sharp focus on my subject, I keep motion in the image. The editor is happy. The readers are happy. I'm happy.
All in all you should opt for the telephoto.