I still haven't found a definitive answer, but I continued my research and came across the following information that may serve as a partial answer.
John Walker discusses the pronunciation of this word in his Critical Pronouncing Dictionary (1791). He prescribes the long vowel, but mentions the pronunciation with the short vowel:
This word is sometimes pronounced with the vowel in the first syllable
short, as if written lĕd-jend. This has the feeble plea of the Latin
Lego to produce ; but with what propriety can we make this plea for a short vowel in English, when we pronounce that very vowel long in
the Latin word we derive it from ? The genuine and ancient analogy of
our language, as Dr. Wallis observes, is, when a word of two syllables
has the accent on the first, and the vowel is followed by a single
consonant, to pronounce the vowel long. It is thus we pronounce all
Latin words of this kind ; and in this manner we should certainly have
pronounced all our English words, if an affectation of following Latin
quantity had not disturbed the natural progress of pronunciation.—See
Drama. But, besides this analogy, the word in question has the authority of Mr. Sheridan, Mr. Scott, W. Johnson, Bailey, Entick,
Perry, and Buchanan, on its side. Dr. Kenrick and Dr. Ash are the only
abettors of the short sound.
Interestingly, he recommends the short vowel for legendary:
As the preceding word has, by the clearest analogy, the vowel in the
first syllable long, so this word, by having the accent higher than
the antepenultimate, has as clear an analogy for having the same vowel
short, 530, 535. This analogy, however, is contradicted by Dr. Ash, W.
Johnson, Mr. Scott, Entick, Buchanan, and Perry, who make the vowel
e long, as in Legend. As Dr. Johnson's accentuation does not determine the quantity of the vowel, his not inserting this word is,
in this case, no loss ; but Mr. Sheridan's omission of it deprives us
of a valuable opinion.
So this establishes that the modern pronunciation existed at least as early as 1791. I still don't know how late the pronunciation with a long vowel was used (although the citation from Skeat in my question gives a lower bound of 1891).