Position is very valuable in this game. If you have position on your opponent(s), you get to see how many cards they discard before having to make a decision.
Negraneau did a section in one of the Supersystems that goes into quite a lot of detail... also there is a newer book by Ken Lo called mixed games that covers it very extensively... I love 2-7T myself
Sorry, i don't have any advice on this game, just discovering it myself too, But I just wanted to say that it's indeed a beautiful and also fun game!
Hopefully I'll pick up some tips here too