Isn't the third of the second line a minor IV? (In your hypothesis Dr)
yesss, I would have interpreted it that way, as a modal interchange: IV "borrowed" from the parallel scale (a term which, moreover, I have never particularly loved).
I would say IV VII, followed by III VI in progression
Me too, although I have always thought of something curious (and a bit twisted): in modal interchange, there is a tendency to replace an chord with the equivalent degree of the parallel scale, preferably with the same function; which works for all degrees except for the seventh (which in the natural minor scale does not have a function exactly corresponding to the VII of the major scale). For example, in DØ G7 C∆ we can derive the DØ from the minor II, maintaining the function of preparing the V.
But thinking that F-7 Bb7 C∆ originates from F∆ BØ C∆ is difficult (not impossible, but let's say unlikely in jazz or pop harmony).
Line 4 convinces me very little; A7 smells like a V of D-7, which is the second of C major, it touches the fifth... precisely G7, and that G-7 in my opinion is a V-, which is also used in classical contexts, all cadencing to I (F major)
My hypothesis is that the bVII7 can indeed be interpreted as a pure interchange, but also as a continuation of the iv minor, with a simple bass movement, somewhat like what happens in a tritone substitution. In other words, if we keep Bb- instead of Eb7, the piece does not undergo substantial changes.
Line 4 convinces me very little; A7 smells like a V of D-7, which is the second of C major, it touches the fifth... precisely G7 and that G-7 in my opinion is a V-, which is also used in classical contexts when cadencing to I (F major)
Perhaps if I simplify it like this, I make the idea clearer (let's imagine that the original was like this, poor Henry, and that the changes were made subsequently):