re: "There's one huge, gargantuan, omission on this: a statement that says the output of the tool is the outcome"
I think the way to cover yourself will be to append the output from the tool to any contract, so that they become part of the agreed contractual terms. Also ensure that any statements about supply are consistent with the answers given to the tool.
Whilst this doesn't prevent HMRC from changing their minds, it does provide evidence that your legal team can use to challenge HMRC and show you were acting in good faith...