I hate to harp on this, but I think this is better understood if you keep track of which MODE they are in. You can't conceptualize this only in terms of Major-Minor.

1) When Phish jams in minor, it is almost always DORIAN with a focus on the minor pentatonic notes - and the dorian notes added for color - Carini (Em), Ghost (Am), Tweezer (Am), Sand (Am), Bowie (Em) - all Dorian. An interesting exception is Stash (D natural minor, or Aeolian) - when Stash goes to F - it REALLY is doing a modulation to the relative major. (what you call MODIII). But this kind of shift is actually rare in Phish jams I'd argue because they're almost always in Dorian.

2) So I like to to think of Phish "minor" jams as modal jams focused in on the "ii" chord. This means a shift in Ghost from Amin to Dmajor is not really a I-IV as much as a ii-V. (dorian-> mixo). If it were really A natural minor to D major, the pitch collection would modulate to change notes C and F to C# and F# respectively - which would sound weird. The "ii"-> "V" pulls off the Amin-> Dmaj feel within the pitch collection/key at hand (G major). This is also present in the many examples you have of Amin-> Cmaj - that is usually a shift from dorian to lydian (ii-> IV, not i-III) in the Gmajor family of notes (the F# persists).

My only point is, all your tables really only keep track of whether the jam is 'minor' or 'major' but really matters is what MODE they are in - Dorian? Mixolydian? Aeolian? If you understand the mode, the next chord that comes is usually within the chords of that mode understood as: I ii iii IV V vi vii I

3) Phish major jams are almost always either Lydian (Reba, Curtain, Wingsuit) or Mixlydian (DWD, Jibboo, Gin). In other words, they are almost always playing with the IV-V chords of a given key. So when Disease shifts from A to G, it's not really fair to call that a I-> flatVII. It's better thought of as just a V-> IV. Hood is an exception which is really in Dmajor (I). A lot of Hoods recently have modulated to D mixloydian which brings the C-> D major chord feel into play (again IV-V).

Anyway, this is awesome stuff - thank you for your posts. I hope my ideas are helpful and not annoying. :-)