I just felt a bit unsure about the F minor part
then there's the part around 3:00 with the F7-Am/E-D chord progression, where it also sounds to me like it's changing key for a second. But maybe I should just ignore that.
What makes you unsure? Asking in the interest of challenging your brain I see a pretty neat modulation from A major to F minor, ending with a D64-53 cadence, but then he launches into the F major section basically like a Picardy third.
He does some cool harmonic progressions that basically lead back to where he started occasionally. Could you maybe post a screenshot of the passage just so I can be sure what you are talking about? The recordings I'm referencing have different timings than yours