Once they train up to a certain level, they'll start sparring with each other (just like they did in the past), and sparring dwarves seem to level up quite rapidly.
Definitely has nothing to do with it. They'll spar at any skill level, as long as the two combatants are relatively equal. Legendaries typically won't spar with raw recruits, but accomplished will spar with talented; I've seen it many times before. No amount of waiting is ever going to increase the rate at which a squad spars; if they've got basic skills they start sparring, and that's as fast as you'll progress for that size squad.
In other news, the issue here is you have a 10 dwarf squad. Break it up into three 3 dwarf squads and you'll train three times faster because each squad can only have one sparring match going on at once. With three dwarf squads you get almost non stop sparring from all members and it trains really fast. With a ten dwarf squad you'll only have one sparring match going on at once and it progresses at a snails pace. It's not intuitive in the least, but it is the way it is.
The danger room is insanely effective. Using it, you WILL get Legendary+5 shield users all across the board in approximately a year. A legendary +5 shield user is essentially immune to all attacks -- five years after hitting that rank in my current game after dozens of fights and once using the squad to take out an entire siege by themselves (six goblin squads plus two troll squads vs. 12 dwarves, mostly 5x legendary) these dwarves have not taken a single hit since. Not one hit. It feels almost like cheating. They're still vulnerable to many special attacks (deadly dust foremost, of course), but conventional enemies can't even touch them.