Generally LOL XI is the most efficient option for fragment events - the drops are much better than LOL X, and it works out better value than LOL XV because you can get over twice as many runs for the same amount of sands.
That being said, 600 runs alone of a dungeon in 3 days is really pushing it to get all the event achievements and the 3,500 frags for the T3 is clearly designed to get players buying frags. I don't have a set of Brave either and I want one...