Thanks to Joe Dubin's New Breed-bred eagle eye for such things (though discounting the Odd Couple game we won only in fiction), it appears the Mets' winning ways date back further than originally thought, all the way to June 13, 1967, a full 44 games before the juncture initially calculated (when I was either too sleepy or too timid to wade through what loomed as a full and daunting pallet of L's on baseball-reference [1]).
Commencing with that evening's doubleheader split against the Reds at Shea, specifically rookie Tom Seaver's eight-hit complete game 7-3 victory over Cincinnati in the nightcap (the fifth win of the young man's career), the Mets were 22-22 up to and including the aforementioned July 28 loss in Los Angeles…meaning that since the middle of play 6/13/67, the Mets are 3,308-3,307 (winning percentage: .50007559), marking the furthest you can go back in time and call the Mets cumulative winners. Before the second game of that June 13 twinighter, up to and including the 6-0 shellacking the Reds pasted on Bill Denehy in the opener, the Mets were 277-582 (winning percentage: .32246799).
The larger points stand as previously reported [2]:
• The Mets were very bad well into their sixth season, covering a period of their first 859 games.
• They've been intermittently almost as bad since then but sometimes they've been pretty good and once in a while magnificent. Thus, for more than four decades, they've been the slightest shade over middling in a span that covers 6,615 games, right through last September 28's 4-2 defeat at the fins of the Marlins.
• They still need to win 82 games this season to have as many yearly winning records as losing records in their checkered 48-year history.
• They will still have an all-time losing record even if they go thirty games over .500 every year for the next ten years.
• Buy my book please.