I recommend taking a wizard with school of divination along - you can rewrite couple rolls with a pre-generated number!
Wow, that was painful. It was so difficult hearing him reach around at a snails pace to get to an incredibly obvious point, while still missing the greater point.
On point you need to throw somewhere between 3 and 5 decks of cards into your system to avoid it causing much bigger problems than it solves and the better solution for this is to just seed the RNG.