Jack - no argument on your analysis.

One of the 'tricks' for understanding how tunes get 'transformed' is that of 'note substitution'. Octave swaps(@@@) are the most common, but fifth (and fourth - depending on your viewpoint!) swaps are easy too, especially on some instruments.

(@@@)
After the octave swap has occurred, a common path of growth of difference is to start modifying the notes next to where the 'swap' took place (think twiddling your fingers on a whistle). This 'growth path for change' can also occur around the fifth 'swap'.

"acquired a few decorative F sharps"

When a tune 'changes instruments', some 'accidentals' are easy to add for decorative twiddles depending on the new instrument being used.

As for what 'mode' it is in NOW, it ain't!

It has become, for want of a better word, what some may wish to call, 'multimodal!!!' - or you could just say that it 'has evolved its own particular gapped scale'...

One CAN get too pedantic! :-)