Ah I love this sort of game. They remind me of pin games in that if you don't know the optimal strategy (in this case, trash treasure ASAP) ahead of time, then you are at a big disadvantage. Example:
http://councilroom.com/game?game_id=game-20120216-124135-cdaed189.html.
I played a KC-Possession game once where Ambassador and Lighthouse were also present, which created for a pretty funny log:
http://councilroom.com/game?game_id=game-20120224-145540-4774e41f.html Winnower plays an Ambassador.
... Lighthouse provides blueblimp immunity to the attack.
... Winnower reveals a Province.
... returning it to the supply.
[...]
Winnower plays an Ambassador.
... Lighthouse provides blueblimp immunity to the attack.
... Winnower reveals a Province.
... returning it to the supply.
Guess I shouldn't have played Lighthouse on my previous turn!