I'm not sure that this is enough as it is stated here and in the original comment. There may be a technical solution that allows it to be done in one go, but an

I'm not sure that this is enough as it is stated here and in the original comment. There may be a technical solution that allows it to be done in one go, but an alternative would be to do the count, have a window in which the count can be challenged and then do the draw in a pseudo random deterministic way with seeds coming from a number of sources (e.g. different candidates).