If I may provide some constructive criticism as someone who also has a background in tuning and tuning theory: I believe the article is pretty cool and you clearly have a good background on modern microtonal music. However, it is also clear that you do not have a good background on historical tunings (there are some factual errors in this regard).
Modern sources often implicitly assume that you understand tuning theory before teaching it, I agree. The understanding they often expect is this historical theory, though. I find that understanding historical tuning based on the idea of scales to be sort of tough to understand, while the circle of fifths is a lot more useful, and before 1900, pretty much nobody wrote about tuning in terms of scales since for all practical purposes it is very easy to hear frequency relationships in fifths and fourths rather than hearing them from steps.
Just Intonation is built on top of the harmonic series (not the circle of fifths), and I would suggest that you introduce the concept of the harmonic series before thinking about scales and fixed temperaments (your "boring" solution). As someone who does understand Just Intonation pretty well, I found the idea of going straight to a concept of scales very confusing, personally. The scale for true just intoned tunings is built on top of the harmonic series relationships you showed later, and those don't all have nice intervalic ratios.
Factually, the intervals were wrong for a typical Pythagorean scale: your fifth is 2^18/3^11 when the correct relationship for the typical notion of Pythagorean tuning is 3/2. Your scale stacks fourths based on 4/3 relationships, leaving the most important interval in the scale as the so-called "wolf" fifth. Most practical notions of Pythagorean tunings used fourths going one way and fifths going the other from the tonic, leaving the F#-C# relationship as the "wolf" (if the tonic is C), while all other fifths are pure. If you illustrate this with a circle of fifths rather than a graph showing scale degrees, it's a lot easier to understand. Pythagorean tuning also isn't really a type of just intonation since it doesn't use a harmonic series on a single note, but the exact definition of "just intonation" varies by source (some would say that even a temperament like Werckmeister is "just intonation").
All that said:
I would suggest you start with some ideas about tuning, introduce the harmonic series, introduce that "just intonation" is about preserving harmonic series relationships, and then go straight to your "freestyle" section. Eschew the notion that you need to understand the history of unequal temperaments to understand the present concept of the tension between the equal-tempered compromise scale and the just-intoned harmonic series.
Since you're more interested in modern theory, and your innovation and interests are there, I think you can skip the history and just get straight to the math and the lattices. Whether you use circles of fifths if you do this is up to you (I'm guessing you shouldn't - they are not so useful for modern tuning ideas).
Thanks for bringing in your understanding of historical tunings. Maybe a simpler correction would be to describe the example as "a Pythagorean tuning" rather than "THE Pythagorean tuning", which would be (according to some) technically correct despite not being historically representative. The goal of that example isn't to provide historical background, it's to provide one of the simplest possible derivations of 12 usable tones from just intervals. I believe that that the 3 being a multiplier or a divisor is a matter of perspective: if you start from the last tone in my example, the same scale is derived from reversed fractions. Starting from the middle might be closer to what you're describing, hopefully I'm getting that right.
Grounding the whole thing in the harmonic series on would certainly make sense.
You are correct about the ratios not mattering that way, but it is jarring for someone who knows about this stuff to see 4/3 (the fourth) instead of 3/2 and to see the positioning of the wolf being the I-V relationship in the scale. I would suggest that if you want to keep it, you should be explicit that the frequency relationship on this fifth is far off, and I would suggest drawing a circle of fifths (which will be a lot more clear after seeing a fifth in the harmonic series). Instinctively, that section feels very wrong despite being (mostly) right. I would personally suggest dropping it entirely - you don't need the history.
Edit: I was thinking about your existing diagram a bit more, and here is the rework I might suggest without doing anything too major:
Do an up-a-fifth-down-a-fourth path through the chart, and that is easier to rationalize and understand than "mostly 4/3 with 2/3 ratios interspersed when we need to drop an octave":
C * 3/2 -> G
G * 2/3 -> D
D * 3/2 -> A
A * 2/3 -> E
E * 3/2 -> B
B * 2/3 -> F#
There is only one break from the pattern right here with two descending perfect fourths in a row:
F# * 2/3 -> C#
C# * 3/2 -> G#
...
You can also restart from C going down to F and Bb once you reach F# and that gives you the typical Pythagorean tuning, but then you will have to explain why that happens to readers who are unfamiliar with tuning.
Modern sources often implicitly assume that you understand tuning theory before teaching it, I agree. The understanding they often expect is this historical theory, though. I find that understanding historical tuning based on the idea of scales to be sort of tough to understand, while the circle of fifths is a lot more useful, and before 1900, pretty much nobody wrote about tuning in terms of scales since for all practical purposes it is very easy to hear frequency relationships in fifths and fourths rather than hearing them from steps.
Just Intonation is built on top of the harmonic series (not the circle of fifths), and I would suggest that you introduce the concept of the harmonic series before thinking about scales and fixed temperaments (your "boring" solution). As someone who does understand Just Intonation pretty well, I found the idea of going straight to a concept of scales very confusing, personally. The scale for true just intoned tunings is built on top of the harmonic series relationships you showed later, and those don't all have nice intervalic ratios.
Factually, the intervals were wrong for a typical Pythagorean scale: your fifth is 2^18/3^11 when the correct relationship for the typical notion of Pythagorean tuning is 3/2. Your scale stacks fourths based on 4/3 relationships, leaving the most important interval in the scale as the so-called "wolf" fifth. Most practical notions of Pythagorean tunings used fourths going one way and fifths going the other from the tonic, leaving the F#-C# relationship as the "wolf" (if the tonic is C), while all other fifths are pure. If you illustrate this with a circle of fifths rather than a graph showing scale degrees, it's a lot easier to understand. Pythagorean tuning also isn't really a type of just intonation since it doesn't use a harmonic series on a single note, but the exact definition of "just intonation" varies by source (some would say that even a temperament like Werckmeister is "just intonation").
All that said:
I would suggest you start with some ideas about tuning, introduce the harmonic series, introduce that "just intonation" is about preserving harmonic series relationships, and then go straight to your "freestyle" section. Eschew the notion that you need to understand the history of unequal temperaments to understand the present concept of the tension between the equal-tempered compromise scale and the just-intoned harmonic series.
Since you're more interested in modern theory, and your innovation and interests are there, I think you can skip the history and just get straight to the math and the lattices. Whether you use circles of fifths if you do this is up to you (I'm guessing you shouldn't - they are not so useful for modern tuning ideas).