Truth: Dozens of Rishonim and Achronim have said explicitly that Chazal were, at times, wrong about various matters, and they have gave us explicit permission to follow our brains and the evidence on any question that doesn't touch halacha. Though some pretend that this idea is contained only in a few obscure sources, or based on questionable readings, the truth is that its a widespread opinion and one that is stated many times and in unambiguous language.
(2) Claim: The academics who give Mishlei a late date are using a "non-Orthodox mode of thought" which poisons their conclusions.
Counter argument: Any statement about the attitudes or outlooks of the academics is purely speculative. We have no information about what these particular academics thought about the Sages or the Mesorah. We know nothing concrete about their "mode of thought." Moreover, whatever their "mode of thought" may have been is entirely immaterial to the quality of their evidence and the strength of their arguments. To suggest that evidence can't be considered because it was accumulated by people who are in the grips of the wrong "mode of thought" is an ad hom argument, akin to rejecting Euclid's math on the basis of his paganism.
(3) Claim: To say that the anyone other than Solomon wrote Misheli is to say that Chazal were incompetent at collecting and assessing information.
Counterargument: No it doesn't. To say that anyone other than Solomon wrote Misheli is to say that this one, lone, solitary claim was never investigated properly, and not because Chazal were mentally deficient, but because the necessary tools were not available to them.
(4) Claim: To say that the anyone other than Solomon wrote Misheli is to undermine the authority of Chazal
Counterargument: It doesn't follow from the fact that Chazal may have been wrong about one, solitary, thing that they were also wrong about everything. Besides, the Talmud Bavli overflows with statments made by Tanaim and Amoraim that were, at some later point, determined by other Tanaim and Amoraim to be untrue, or inaccurately transmitted. That fact that Chazal frequently make corrections to the tradition they inherited, strongly suggests that shortcomings in the accuracy of the Mesorah were recognized by Chazal themselves. [One of perhaps hundreds, if not thousands, of examples] Why should we deny what they admit?
(5) Claim: To say that anyone but Solomon wrote Mishlei is to undermine the Mesorah
Counterargument: To the best of my knowledge, only one lonely brysah makes this claim. There's no reason to think that this opinion was widely accepted by other Sages, and there is no evidence at all that this opinion was ever considered an essential, infallible part of the Mesorah. And, even if we stipulate that it was, evidence-based criticism of one small, tiny, little speck of the tradition is not the same as wholesale denigration of all of it.
(6) Claim: To say that anyone other than Solomon wrote Mishlei is to undermine the Oral law stretching back to Sinai.
Counterargument: Solomon lived several hundred years after Sinai, thus any tradition about his activities can't possibly be part of the original, from-Sinai Mesorah. (quoting Anon:) "A tradition about the authorship of a post Sinai book is [therefore] categorically different from a tradition about halacha that does go back to Sinai. So, how can you claim that rejection of a claim from one category of tradition is identical to the rejection of the whole of an entirely different category of tradition?"
What do I believe? Proverbs is an anthology of different Wisdom collections, assembled over time by various authors and editors. Some specific ideas, if not the text of some specific Proverbs may have originated with Solomon or his court, but it seems most unlikely the whole entire book can be attributed to him.