There is nothing wrong with using singular and plural subjects in different clauses in the same sentence: as you yourself observe, we can say things like "If there are three of an unparalleled thing, is any one of them truly unparalleled?"
I think the reason for uncertainty about whether "any of [plural noun]" should take singular or plural verb agreement is because the noun in the prepositional phrase is plural in form, but the word any is not, and semantically it could be considered either singular or plural. For comparison, the construction "which of [plural noun]" takes singular or plural agreement depending on its meaning: we could say "Which of these squares is red" or "Which of these squares are red" depending on whether we expect a singular or plural answer.
Apparently, both usages are fairly common, but it's more common or more commonly accepted to use a singular verb with "any of [plural noun]". See CowperKettle's answer to the question "How to use “any of”" on ELL SE:
I did some googling, and it turns out any of your options is admitted: here's a link to [a grammar blog post]. I quote:
Any of can be followed by a verb in the singular or plural: "If any of your friends want/wants to come, they are welcome." (Plural is preferred in everyday language, singular is more formal)
Or, as the same issue it treated in [a grammar rule sheet] at a New Zealand university site,
When any of is followed by a countable plural noun, the verb can be in either singular or plural form, but a singular verb is more common in a formal style: "If any of your friends is/are interested, let me know."
Unfortunately, both of the links seem to be broken, so I haven't reproduced them.
I found a post with a relevant quotation from the archive of the Pearson Longman Grammar Exchange Questions and Answers Newsgroup. Rachel posted a message with the following quotation (I have not checked the quoted source directly):
"When none, neither, either and any are followed by "of + plural noun/pronoun," they are normally used with singular verbs in a formal style in British English. Plural verbs are common in informal British usage and generally in American English.
None of the cures really works. (formal British)
None of the cures really work. (informal British; American)
Neither of my brothers has/ have been outside England.
Has/Have either of them been seen recently?
If any of the children gets/ get hungry, they can have an orange."
(Michael Swan, Practical English Usage, Second Edition (Oxford University Press, 1995. Page 534)