"Character minimums hurt your entropy too."

Not really. If X is the number of characters your password can be made up of, there are 8^X possible passwords that are 8 characters long, and 8^X-1 possible passwords that are less than 8 characters long. Even here, right on the border, you've only lost 1 bit of entropy (half banned, half allowed), and you win big the moment someone makes it even one character longer than the minimum who wouldn't have otherwise.