[T]hree sources ... say that they've read the whole General Prologue and can't find anything remotely similar to the "government of the people ..." quote.
For example, see Wolfgang Mieder, Proverbs are the Best Policy: Folk Wisdom and American Politics, Utah State University Press, 2005: Chapter 2, "Government of the People, by the People, for the People": The making and meaning of an American proverb about democracy: p. 16: "The British journal Notes & Queries included several short paragraphs between 1908 and 1916 on the phrase, starting with the question whether anybody could verify the claim that John Wycliffe included the following declaration in the preface to his Bible translation of 1384: 'This Bible is for the government of the people, by the people, and for the people.'[fn2] This matter came up again in 1916, but once again nobody was able to find the statement in the various editions of the Wycliffe Bible."
FN2, p. 248-249: "Dewitt Miller, 'Abraham Lincoln: Wycliffe Bible,' Notes and Queries, 10th series, 9 (1908), 10. The claim was made by Ward Hill Lamon, The Recollections of Abraham Lincoln (Chicago: McClurg, 1895), p. 176 ... I have checked the entire preface of the Wycliffe Bible, and the statement is nowhere to be found."
See Also Stephen Booth, Precious Nonsense: The Gettysburg Address, Ben Jonson's Epitaphs on His Children, and Twelfth Night, University of California Press, 1998, p. 33: "Lincoln scholars have long hoped to find a specific source for the prepositional triad in government of the people, by the people, for the people; they have not found one [fn 7], but the number of similar locutions they have come up with testifies both to the cause and the justice of their search." FN7: "Mark Womack points out to me that The Columbia Dictionary of Quotations (New York, 1993) gives the following s.v. "Bible": "The Bible is for the Government of the People, by the People, and for the People" and cites its source as the "General Prologue to the Wycliffe Translation of the Bible (1384)." The Columbia Dictionary's confidence about the date and its apparent indifference to the distinction between the early version of the Wycliffite Bible and the later one are surprising. I have not found the quoted sentence in any printed text of any of the Wycliffite prologues."
Finally, see also Hoyt's New Cyclopedia of Practical Quotations, Completely Revised and Greatly Enlarged, by Kate Louise Roberts, New York: Funk & Wagnalls, 1923. p. 332, "The phrase 'of the people, for the people and by the people' is not original with Lincoln. There is a tradition that the phrase, 'The bible shall be for the government of the people, for the people and by the people,' appears in the preface of the Wyclif bible of 1384, or in the Hereford Bible, or in a pamphlet of the period treating that version. See Notes and Queries, Feb. 12, 1916, p. 127. Albert Mathews, of Boston, examined the reprint of 1850 of the Wyclif bible, and finds no reference to it."
I did find a print version that included the whole text of the General Prologue to the Wycliffe Bible, edited by Josiah Forshall & Frederic Madden, Oxford University Press, 1850 (in 4 volumes). I read the Preface and there is no reference to any such quote. I read the supposedly "controversial" chapters referenced in the Dove book, below, but found nothing similar.
I looked at the sections on Wycliffe in the following books and found nothing referring to the quote:
Benson Bobrick, Wide as the Waters: the Story of the English Bible and the Revolution in Inspired, New York: Simon & Schuster, 2001
Margaret Deanesly, The Lollard Bible and other Medieval Biblical Versions, Cambridge University Press, 1920
Mary Dove, The First English Bible: The Text and Context of the Wycliffite Versions, Cambridge University Press, 2007
F.F. Bruce, The English Bible: A History of Translations, London: Lutterworth Press, 1961.
I did see all the info on the internet, including the Wycliffe organization, stating that Wycliffe had made this alleged statement. However, if so, it's odd that none of the books above would mention it. The Preface to the Forshall & Madden 1850 reprint mentions earlier writings of Wycliffe, some of which are quoted, but none of those mentions the alleged phrase, either. One of those writings (a commentary on Luke) includes the phrase: "Crist Jhesu, for thyn endeles power, mercy, and charitie, make thi blessed lawe knowun and kept of thi puple, and make knowun the ypocrisie and tirauntrie and cursidnesse of Antecrist and his meynee, that thi puple be not disseyued by him." But that's a big stretch (and missing 2 prepositions).