July... rhymes with coolly.

Suddenly, it's July, and I wonder if you're pronouncing the word correctly. The (unlinkable) OED says:

The word was usually stressed on the first syllable in the early modern period, as the form July-flower, due to folk etymology (see γ forms at gillyflower n.), implies. The orthoepists Peter Levins (1570) and Elisha Coles (late 17th cent.) both include the word among those which have unstressed -y, and Johnson (1755), W. Johnston Pronouncing & Spelling Dict. (1764), and J. Walker Dict. Answering Purposes of Rhyming (1775) all indicate stress on the first syllable (Johnston also marking the y as ‘long’). Both occurrences of the word in Shakespeare are so stressed, as are most metrical examples down to the late 18th cent..... Stress on the first syllable still occas. occurs in Scotland.

That's authoritative, even though the simplest Google detects an error. There are 3, not merely 2, occurrences of "July" in Shakespeare:

The Winter's Tale: "He makes a July's day short as December..."

Much Ado About Nothing: "The sixth of July: your loving friend, Benedick."

King Henry VIII: "And proofs as clear as founts in July when/We see each grain of gravel..."

We know these plays are written in iambic pentameter, so these lines prove the stress went on the first syllable. Who put the lie in July... and why?