I have a hard time thinking of anything UUs generally hold to in terms of doctrine at all

Well, UU is definitely on the "accommodationist" side, which means that, when asked "Are there supernatural things?", it answers "Shut up, debate is intolerance". But Unitarians' behavior does reveal a probability estimate - for example, someone praying for a disease to be cured is certainly putting a non-negligible probability mass on "There are things that listen to me pray and can cure disease". There are no Official Unitarian Beliefs, but there are beliefs of individual Unitarians and they can be stupid but protected by "Don't tell me this is stupid or you are evil and intolerant"-type memes. In particular, "Belief in the supernatural is not laughably wrong" is a claim made by many Unitarians.

rabbits chewing cud

Okay, chewing pellets could plausibly be lumped in with chewing one's cud, though I am Not Happy about things becoming "imagery" the second they're literally false.

Yes, science can prove dead people cannot rise again... but it cannot prove that an agent with the power to suspend or violate the laws of nature could not perform the trick.

Well, obviously such an agent could. But science can and does prove that such agents just don't happen. We've spent the last three thousand years looking at increasingly robust laws of the universe, and we found out that the universe loves locality and referential-independence and hates special exceptions. We've spent the last thousand years looking at accounts of miracles and never found one that held water. At some point you just reach probabilities lower than "There is a pony behind my sofa, but it teleports away whenever you try to look at it, by sheer coincidence".

To accept most scientific claims ("Schrödinger's equation predicts...") and also accept a claim that contradicts their generalization ("And lo, Jesus did violate conservation of energy") requires rejecting the claim "Induction works", which is sort of the very core of science.