Well, since this came back to the top I'll give another update.
If you give them enough nest boxes, these things apparently breed like rabbits. I now count 54 of them:
I had been keeping them in the large room in the lower right corner with a bunch of nest boxes, but their population was starting to get a bit out of control, so I shut it down and roped them up in separate rooms.
Also, another problem arose. Occasionally, the dragons will become unchained/unpastured after training and decide that they want to see my dining hall, where they would inevitably encounter my military and probably immolate a few civilians during their battle. Thankfully, I found a solution. I put a pressure plate over the exit to the room set to detect citizens and creatures larger than 100,000 (10,000 on the pressure plate construction list). Since all of my dragons are greater than 3 years old by now, any dragons that wander out will trigger the pressure plate and cause a floodgate to close, sealing it in, usually along with the trainer who released it. The trainer will take the dragon back to its rope, so I just have to periodically check and release any trapped trainers. I may throw a food stockpile in there at some point, though, just to be safe.
I think that this happens because of "failed" training sessions...? I'm not entirely sure, but now all my dragons are trained to masterful and my trainers are all legendary, and it hasn't happened in quite a while.
I may put them out at my front gate behind some fortifications at some point, but for now the front gate is still underdeveloped and surrounded by very flammable wilderness.