The iron trap and improved iron trap you get from the level 2 barn DO NOT share cooldowns. This is mildly useful, but the true exploit is when you deploy both traps on the exact same place and lead a mob over it. You get TWO caged beasts for ONE mob. I do not have l3 barn, but I would guess that if you get another trap from that it would possible allow THREE caged beasts instead of one to be caught per mob.
UPDATE: Even better than I thought. After dropping the first 2 traps, wait out the 15s cooldown, and then drop two more. After they arm, kite the mob over all 4 traps. You have 30s from the time you deployed the first 2 before they despawn.
UPDATE 2: This SHOULD allow you to get 2 elite beasts for 1 using the level 3 trap if you wait out the new shorter cooldown before dropping the second trap right on top of the first trap. I don't have l3 barn so I can't test it myself, but it should work the same way as the other traps do. Needs testing.
This might potentially work in a party if all players drop traps in the exact same location, though I did notice a rapid despawn on the mob when applying 4 traps at once, so somebody with the l3 trap should definitely try this out and report back.