Pre-flop "His min raise doesn’t really narrow his range at all." Nope, your calling is what doesn't narrow his range - you have allowed yourself to play guessing poker - If you 3bet and he calls you have narrowed his range, if you 3bet and he shoves you know exackly where you are. But if you think your hand is too weak to 3bet, then why not fold - you are behind to every Google Page Ranking and dominated by AK, AQ, AJ, AA, KK, QQ, JJ and TT. You have nothing invested in the pot, wait awhile and gain some info on the guys betting before getting involved.

Also why is TT4 a great flop? You were obviously going to win a little bit more or lose a whole lot only KT, QT, JT, T9 would have given you action and still be behind, and each of those had outs - good players would have folded KT, QT, JT and T9 if the beting got really serious and they didn't improve.