I really like the badges/medals idea. It would certainly give people a reason to keep playing. But what about rewarding persistent players with something they can use like an increased chance to find uniques or (even better) a wider available selection of uniques when they achieve higher ranks and/or certain badges? In other words maybe certain uniques could be "unlocked" by playing the game more and more.
Also, this could be a bit more of a long shot, but how about adding a type of currency that you could use to purchase items or additional traits at the start of the game and you accumulate it by playing the game over and over? The currency you earn in each game could be based on your score or your achievements in the game. For example, maybe clearing out certain special levels result in extra earned currency. I think this would increase replayability for those who like the game but are bad at it (me) because the more you play the better your chance of winning. Of course, in order not to tip the balance too favorably toward the player, care would need to be taken so that the benefits are not compounded or perpetual, but rather they could be utilized every now and again.
Just tossing it up there to see if it sticks. Any comments?