I would suggest the simple ne falsum quidem, which is quite literally "not even false".
I have been trained as a physicist, and the phrase "not even false" in the field — Pauli was a physicist — is almost exclusively used in isolation, not prefaced with "not only wrong".
Without knowing the origin of the phrase or the typical uses, the English phrase "not even wrong" can be confusing.
I think it's better not to explain it in translations and leave it as succinct as it is.
Depending on the gender and number of what you are referring to, it would be ne falsus/falsa/falsum/falsi/falsae/falsa quidem.
Do ask if you have a specific use case in mind and wonder which choice is most appropriate!
I went with neuter singular, which is good for referring to a single abstract (unnamed) thing.
The translation of "not even X" is ne X quidem, always with ne instead of non.
See Allen & Greenough 217(e).
Finally, I should point out that I wouldn't think of "not even false" as a fallacy.
It's simply a way of pointing out deeper flaws in reasoning.
Your answer to a question can be true or false, but if you have studied the wrong question, it makes sense to say that the answer is "not even false" — irrespective of whether the wrong question was answered correctly.