Francis Meres, praising some of Shakespeare's comedies in 1598, specifies
Gentlemen of Verona, Errors, Love labors lost, and
Love labours wonne, Midsummers night dreame, and
Merchant of Venice. In 1953, a portion of a bookseller's list,
recording some sales from August of 1603, turned up as part of the
binding for a book published in 1638. This list, though not mentioning
Shakespeare, cited marchant of vennis, taming of a shrew,
knak to know a knave, knak to know an honest man, loves
labor lost, and loves labor won.
So this comedy was published and could still turn up. Like many quarto editions, it was probably published without an author's name, and so ignored for centuries. Many speculate that it may have been revised and that we do have it, under another name. If Love's Labor's Lost as we have it is close to its own original, and if Shake-speare was as extensive with a revision of its sequel as he was in turning A Shrew into The Shrew, or Famous Victories into the Henry IV and V plays, then Much Ado About Nothing may be a good candidate (e.g., Ogburn and Ogburn 201; Farina 44). Benedick and Beatrice do have a shadowy backstory. Asimov suggests All's Well That Ends Well unconvincingly (Asimov 606), but Oxfordian E.T. Clark also thinks Love's Labour's Won was the first of three titles: it became The Rape of the Second Helene and then All's Well (Clark 304; cf. Farina 77).
At any rate, until any of this is better evidenced, keep checking Great-Aunt Flossie's attic.