I recently read The Lost Beatles Photographs The Bob Bonis Archive 1964-1966 by Larry Marion (!t [HarperCollins] publ., 2011). Bonis was the tour manager for all three of The Beatles' U.S. tours. He loved photography and took almost 900 photographs of John, Paul, George and Ringo. I pored over the photographs and have grimly concluded that Paul (and John) never made it to America on the 1966 tour.
In the mockumentary about The Beatles, The Rutles All You Need Is Cash, they interviewed Mick Jagger. He said that The Beatles played so far away from the fans that they could have put anyone on stage and who would know the difference? I believe that is what happened to Paul (and John) in 1966.
The common timeline of Paul disappearing has been sometime in September, 1966. From what I saw in these photographs, I would push back the date to AUGUST, 1966.