In brief, the Enharmonic scale is very connected to the Diatonic scale. It uses Diatonic martyries and intervals and the Enharmonic intervals are generally indicated with the Ajem on Ga or Zo, the general Zo flat, and/or sharps on Vou. In that example I was imagining how we would execute that section without the symbols indicating Enharmonic intervals.
This is because this does happen. In fact the Sticheraric genre of 3rd Mode moves back and forth between Diatonic intervals and Enharmonic intervals. While we say 3rd Mode characteristically uses the Enharmonic scale, the way it is written is more like it is an aberration of the Diatonic Scale.