theprestige
Penultimate Amazing
It's only a "motte-and-bailey shenanigan" if it's untrue or irrelevant. In which case instead of rephrasing it into a straw man, just say that it's untrue or incorrectly reasoned. This avoids poisoning the well when it's the facts that should be examined.
We've examined the facts. That's how we know for a fact that the water in the well is toxic. It's not poisoning the well to crack wise about the poison that's actually in the well.
If your examination of the facts leads you to a different conclusion, I'd like to know what it is, and how you reasoned from the former to the latter.
If you're still examining, and haven't reached a conclusion yet, I wish you well on your journey. Watch out for the poison.