Just a note ot two on the 'fixed' chords. Whilst I've no wish to challenge any of the chord names you use they do present the problem that any other version or inversion of them in this context is less likely to sound right.
The chord naming convention we now have came to it's full flower in the twentieth century. In the past there have been other conventions. In the Baroque era figured bass was used where a bass note was given in the score and coded numbers beneath them give intervals for keyboards to add. This is still taught today but I suspect it would struggle with the kind of harmonies found in most current jazz.
An earlier, vernacular and vastly different approach to harmonies was drones. I spent several years playing traditional tunes with a piper. I played fiddle and he played Northumberland Small-pipes. If I remember correctly he had three drones. These were usually set to root, fifth and octave root. He could have all three on at once or any one or two. Every note in a tune would have a harmonic relationship to the drones but I'm not sure that there would be any point in naming them as chords. Occasionally a guitarist would join in with chords but not to any great improvement. Waters got muddier.
It seems to me that this tune, from the bouzouki, is more drones based than conventional harmony based. So where I put B, C# and G# these were strong bass notes over the drones.
As long as the shapes work I'm not that fussed about the names. Drones are used a lot today in modern versions of traditional music. Perhaps the genre will develop it's own specific naming conventions.
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