The diving problem could be fixed pretty quickly. Blatant dives (e.g., diving when there wasn't even a foul committed) get yellows, and make an obvious dive in the box in an attempt to get a PK is a straight red. It is an attempt to fool the referee to get a great goal scoring chance that dramatically affects the outcome of the game, and should be treated as such. If they think that's a step too far, then have folks review fouls after games for dives and hand down suspensions.
The risk/reward for diving is all out of whack and needs to be brought into balance. If they aren't going to enforce rules against diving, it's virtually no risk and potentially huge reward.