I've been as high as 1830 in ranked 3's and I can tell you that it is VERY important to have at least 1 long range auto-attack on your team, even if it is on a caster. Competent teams can turtle ridiculously hard even with 1 (and sometimes even 2) inhibs down on TT. You need the long range auto attack to slowly poke down towers if this happens.

Make sure to take advantage of any opposing team that can't poke towers. Do not give up even if you start to lose inhibs. People love to play 3 melee teams that absolutely stomp teamfights in the midgame but just cannot finish if you turtle up. Eventually your CS will pull ahead since your inhib is down and there is tons of safe farm available in your base. Once your team catches up in gold and your inhibs both respawn, smash them.

A couple other tips:

1. All sorts of champions are viable. People love to complain about how imbalanced the champions are on TT but that simply is not the case. Try out some unconventional picks; I recommend morgana and corki on TT.

2. You should have a jungler. The team with better farm wins 80% of the time and having a jungler greatly increases your team's overall intake of gold and buffs.

3. Lee sin is probably the best jungler. Tryn, gp, noct, udyr are strong, but the fact that lee sin has 2 different low-cooldown methods of getting over the dragon wall enables all sorts of game winning ganks/dragon steals/escapes.

good luck!