Hello!
I have a good grasp on "traditional" harmony and understanding of some more "advanced" concepts such as secondary dominant, tri-tone, diminished chords, ...
I'm trying to expand my knowledge on jazz harmonies by taking simple songs and analyzing them. I try to figure out myself what the basic harmony is, and how I could derive the jazzy harmonies that are actuallay used from that.
I'm writing here because there are parts I really have a hard time understanding and I hope that you can help me!
Today I'm posting the 3rd phrase from "O Little Town of Bethlehem", arranged in this way:

The first two phrases were OK but I don't quite get this one.
We are in F major.
Bar 1: Fmaj7: Ok, that's really the most expected and obvious chord to start with (Imaj7)
Bar 1: Bb7: Ok, that's the IV chord nothing too fancy. Except it's a dominant 7, which is slightly unusual... But that sounds fine because it leads somewhere special on Bar 2.
Bar 2: A7: Here starts the trouble. The sus is just a sus resolving, that's nothing fancy. But how/why did we land on a major A chord (III)? My ear tells me that at this point the tonal center has shifted away from F (to A basically?) That's an acceptable explanation to me, and the Bb7 - A progression makes sense as moving down a half-step is really a V7-I in disguise (after a tri-tone sub).
So my understanding is that the Bb7 is the pivot chord shifting the tonal center from F (where it's the IV chord) to A (where it's the IIb chord, i.e. a sub for V7-I).
Bar 3: Bb/A and Bb/D: seriously this is the bar where I get totally lost. Ok, the descending bass line is nice but not obvious. And what are all those Bb chords if the tonal center is A (IIb ??). The progression goes back to A in bar 4, so is this bar just a fancy V7 of A with a nice bass line?
Bar 4: A9sus: We're back at I (supposing the tonal center is A at this point)
Bar 4: A7: resolving the suspension
Bar 4: C11: moving to the V7 of F, which is the obvious way to bring the tonal center back to F, which starts the next phrase in a very obvious way.
Can someone correct my analysis? Also any suggestion on material I could use to better understand this stuff is welcome!
Thanks for your help! I'll soon be back with other chords I don't understand!