Can I say "more funny" or "most funny" instead of "funnier" or "funniest"?

A search of Google Books for the phrases "the more funny" does turn up a few relevant matches, though some of the matches returned are not relevant because they involve the form "the more X, the more Y," where either X or Y = "funny things" (for example), so more in those cases is modifying things, not funny. Still, the admirable G.K. Chesterton, in Heretics (1905) uses "more funny" in a situation where, as far as I can see, he could have used "funnier":

The question of whether Swift was funny in his irony is quite another sort of question to the question of whether Swift was serious in his pessimism. Surely even Mr. McCabe would not maintain that the more funny "Gulliver" is in its method the less it can be sincere in its object. The truth is, as I have said, that in this sense the two qualities of fun and seriousness have nothing whatever to do with each other, they are no more comparable than black and triangular. Mr. Bernard Shaw is funny and sincere. Mr. George Robey is funny and not sincere. Mr. McCabe is sincere and not funny. The average Cabinet Minister is not sincere and not funny.

Likewise, in an 1890 translation of George Sand, Nanon (1890):

When he next came he expected to have been thanked and kissed for it [the gift of a dress and a hat]. Not at all ; she was dissatisfied because her shoes were low and plain,—she wanted high heels and rosettes. This too amused him ; he was always amused by her grand-princess fashions. The more he hated the nobility the more funny he thought it to see this little irreconcilable offshoot from a noble stem, that he could have crushed between his finger and thumb, fly in his face and order him about at pleasure.

And from Graham Greene, Journey Without Maps (1936):

They [African native people] wore uniforms, occupied official positions, went to parties at Government House, had the vote, but they knew all the time they were funny (oh, those peals of laughter!), funny to the heartless prefect eye of the white man. If they had been slaves they would have had mo dignity; there is no shame in being ruled by a stranger, but these men had been given their tin shacks, their cathedral, their votes and city councils, their shadow of self-government; they were expected to play the part like white men and the more they copied white men, the more funny it was to the prefects.

In all three of these quotations it seems possible that the author's (or translator's) desire to retain a visible more to match the more in the parallel construction may have prompted the use of "the more funny."

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A search for the phrase "the most funny" yields fewer matches because there is no "the most X, the most Y" form to encourage its use. But matches do occur, sometimes influenced by other parallel forms. For example, from Scottish Notes and Queries (October 1887):

Bruin's brochure will appear under every advantage as to typographic accuracy and beauty, adorned with the most curious cuts, the most funny and fantastic figures ; the most grotesque letterings, and the most delectable sculptures.

And here is G.K. Chesterton again, in The Thing: Why I Am a Catholic (1929):

In that one extraordinary phrase ["strange heresies and even bearded and wedded clergy," in Truth magazine], The word "strange" is strange enough. The word "heresy" is stranger. Perhaps at first sight the word "bearded," with its joyous reminiscences of the game of Beaver, may appear the most funny. "Wedded" is also funny. Even the "and" between bearded and wedded is funny. But by far the funniest and most fantastic thing in all that fantastic sentence is the word "even."

And from a letter written by Benjamin Disraeli in mid-December 1853, reprinted in Benjamin Disraeli Letters: 1852–1856 (1997):

But the most funny thing of all, & the most delightful is, that Palmn. has contrived to land the Peelites with the Movement party! Remember Gladstone's Conservative Peroration this time last year!

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So in answer to your question, you most certainly can choose to use "more funny" or "most funny" instead of "funnier" or "funniest," and not be alone and unprecedented in your word choice. But as you know, the overwhelming tendency in English runs in the other direction.