Dice can't do everything at once, guys. Here's my suggestion.
Keep dice as MVP awards, although I'd suggest more tiers, as well as making them harder to get. (I don't think newbie games are really MVP-worthy, and a lot of normal games aren't either.)
However, I do like Rajam's idea, but it should be slightly different. Instead of doing it as "number of games active in", make it more of a "percent of games active in", and use a different icon from the dice.
As far as "good play rewards" go, that's more subjective. I wouldn't be opposed to having something like a 1-5 star rating, but how exactly could you accurately rate someone's play? Not to mention there'd probably be hard feelings based on who got what rating and stuff like that. (You could try win percentage, but often your faction wins/loses and it's not your actions that caused it.)