The only possible way that I could reconcile it as being painted by an AE would be an illiterate painter copying from a master copy. Hence the reverse writing.
Or for some reason the painter began with the reed followed by the loop.. Followed by the loop characters.. Followed by the phyle name.. Which seems a rather convoluted solution. Effectively starting in the middle and working out.
The cartouche characters (within the loop) are substantially smaller than the phyle characters, understandably so if they were constrained by a pre-painted loop.
When we write we use the first character as a size datum for the second character and so on.
As an exercise get the pest possible images that you can find and try to figure out, looking for overlaps, the order in which the individual character strokes were made.
The direction of the strokes can be determined by the taper and paint weight.
Just like so many of these things, look at the evidence and make your own decision.