And the group spent two weeks in America doing five performances from February 7-21 (2 for Ed Sullivan on February 9, 1 at Washington D.C., 1 at Carnegie Hall, and 1 for Ed Sullivan in Miami), and 1 week recording songs for the film from February 25-March 1. They recorded 9 songs for the film, and 6 of them made it there. You Can't Do That was cut from the film, and Long Tall Sally and I Call Your Name were on the Long Tall Sally EP. They eventually recorded the title track on April 16.
Filming started on March 2, and ended on April 24.
Your post implies (at least to me) that they recorded the songs for the film in the U.S. That is not the case. All the songs were recorded at EMI. And I think your dates are incorrect. According to my notes, most of the songs for the movie were recorded on March 4, 1964 and most of the other songs that appeared on the British version of the album were recorded June 1st to 3rd, 1964 with the exception of "You Can't Do That", which was recorded sometime between January 29th and February 25th, 1964.
The American (United Artists) version of the album contained 8 tracks + music from the score composed by George Martin. The UK album contained 13 tracks and no score music.