While Toady has been improving the sparring situation, I think there should be another way to train dwarves. All over the world, people have come up with training exercises to help someone learn a martial art. The dwarves should be able to do the same.
The advantages of drilling over sparring are simple: a very experienced person can safely drill a student, students can drill by themselves or with another inexperienced person for approximately the same gain, an instructor can drill a large number of people easily, and students can learn and re-teach the drill quickly.
The disadvantages are also simple: drilling does not promote as rapid of a skill gain as sparring, drilling may become disadvantageous if sparring does not also occur, and drilling will not force someone outside of their comfortable techniques like sparring against a good opponent will.
So, I'd like to propose that military specialists be able to get strange moods and create sets of drills, then a gym or school for teaching their martial specialty. They would be able to teach students to a certain level of proficiency without sparring, then be able to supervise the sparring, supplement it with drilling, and have their students experience more rapid skill gain. (With the new system, this should be applied to basic combat disciplines, too, like dodging, possibly armor/shield using)
The way it would work would be a lot longer than a normal strange mood, and can only be started if there are at least five military dwarves, and there is no enemy in sight. The first part of the strange mood would be for the mooder to grab the highest-level military dwarf in sight, and give him/her the task "Creating Drills". They would spar for a length of time, but drink in between sparring sessions. The sparring here would have a decreased chance of injury, I would think.
After that is done, the mooder would demand a room to construct his/her gym. The room could be no more than, say, 200 tiles total, but he/she would specify the dimensions, possibly by having that show up on the nobles screen. After the room was dug and designated, he/she would ask for so much building material and an architect. The mooder and the architect would talk for a while, with different gym things popping up all over the room. The architect would design these things, then leave. The mooder would build the things, and then open the school.
The mooder would then periodically get task such as "teach school." The mooder would round up everyone studying his/her weapon, then take them all to his/her school where he/she would teach for a day or two, with everyone making rapid skill gains. He/she would then go get a drink, head back and direct any sparring matches that go on for the next week or so. Should the mooder's squad become active, then the mooder would not receive these jobs.