First, no one can tell you how Tzeentch can win. If that strategy works every time then this game would be 'broken'. The game relies on players to act as a balancing mechanism and any strategy can be picked apart by the the collective efforts of other players.
If your gaming group really 'hates' Tzeentch, then when Tzeentch gets close to winning he'd be shot down. Our gaming group isn't very fond of Khorne and we have found many ways to counter him, making Khorne the weakest god in our games (though still winning at times).
Luck is part of CitOW and if OW cards cause Tzeentch to come out ahead, that's okay for me. I hope that the dices and card drawings gave you a hint that this game has some randomness to it. Someone can give you a play by play but you'd just pick it apart and cite luck or players' mistakes as the cause- but that is part of the game.
But to be constructive, here are some ways that helped Tzeentch to win in our games:
Draw as much as you can- As you said, the great cards are few and the only way to get more of them is to burn through your deck. It's satisfying to play Drain Power 3x in a game. So discard the cards you don't like or can't use, every round.
Make the most out of Teleport- You can teleport Khrone's warrior to the ends of the earth or you can go there yourself, but the best plays should hurt multiple players. You can teleport Khrone's warrior from your region into Slaanesh's, where Khrone's already there. Khrone will get one less region for dials and Slaanesh will likely suffer causalities.
Co-exist- When Slaanesh slaps down a Fields of Ecstasy, or if Sue for Peace comes up, those are great places to camp.