Hard to imagine springs breaking on a TT that is that new, but it does on occasion. The OEM plastic bushings can be totally shot in just a couple thousand miles and it's a good idea to replace them with something better from the start.
Did you replace just the shackles or the equalizers also? We installed the Dexter E-Z Flex equalizers and they made a huge improvement. If you think it's good now, you oughta try adding shocks to the TT too. We have 4400 lb springs/axles and along with a Reese DC cam WDH and shocks, it handles like a sports car on the endless twisty & hilly roads in the western states. The Bilsteins on our truck also help. If it were me I'd weigh the TT to see if one side is much heavier than the other and see how that compares to the load capacity rating on those LRC tires.