If you decide to re-draw some of S3 winners use a public verifiable random number generator. You can use hash of a future block as a random number.

First, publish a numbered list of miners eligible for the draw, sorted alphabetically, and the block number 10-20 blocks away from the current moment the hash of which will be used as a random number. Wait for the announced block to be mined, convert block hash to a decimal number, take modulus of the number divided by the number of nominees and you get the winner's position in the list.