I get frustrated with this argument, especially the bolded. It's not like the geometric figure actually has anything to do with human nature, or even the inner workings of the enneagram system. Someone just decided to represent the types in a figure and draw some lines across. I could make some MBTI diagram and it would do the same thing.
What you bolded is not an argument, it is a statement that I made about my own doubts regarding The E, but it's not an argument by any means.
The figure does represent the underlying patterns that exist with The Enneagram personality theory, and the patterns as defined by the symbol are mainly consistent. I understand your frustration in not being able to correlate the patterns that exist within the system with human nature - it's absolutely unbelievable!!!

But there are some seriously accurate correlations and insights going on there, and I've seen it again and again with myself and others.
And even if you like the visual representation thing, our system would actually look more symmetric and parallel than the current system.
As for the so called inconsistency with MBTI, it's only inconsistent if you're stuck between the two ways of understanding it. There's the four dichotomies way (I vs. E, S vs. N, T vs. F, J vs. P), which...well...is just four dichotomies. 2^4 = 16, so that's why there are 16 types. Or there's the functions way, which is more complicated, but basically it boils down to this: there are 8 options for your dominant function, and 2 options for each of those for auxiliaries. 2*8 is 16. Either way, the fact that there are 16 types comes from simple logic..
I think the functions do play an important role with the types, but whether the logic that has been devised is actually accurate to individuals... I am unsure... I've looked through the ordering of the functions as defined by Myers, Beebe, Berens etc, and though I see there is a logic behind this, I am unsure of it's accuracy in regards to defining the human personality; particularly in accurately categorizing individuals with consistency and fluency.
One who doubts The Enneagram may say the same for its logic - there is no definitive evidence for either system, and there may never be. But you still haven't pointed out any inconsistencies that occur within the geometric figure of The Enneagram, specifically which correspond to inconsistencies that exist with the actual personality system. You say that it's arbitrary how the 1758241... continuum is separate from the 3693... continum, but this is merely what makes up The Enneagram figure, it's a nine sided figure composed of three triangles, however two of these triangles don't intersect at one side, nor should they, as each point should only connect to two other points by means of the lines connecting them. The triangle that does have all lines connecting has to be the one with the point facing the very top, otherwise the figure wouldn't have nine points.
It's not that I totally dismiss the MBTI, I can see its merit. In my experience, it is probably the best and most accurate personality typing system besides The Enneagram. That is my personal opinion, and only my personal opinion.
With enneagram, the 9 types are all separately defined. There's no multiplying things together to get 9 or anything. It just happens to be 9. The point of our revision is to make 9 actually mean something, namely, the intersection of two variables with three possible values each (3x3 = 9). The variables themselves are the groupings you mentioned earlier. So to type someone in our system, you just have to figure out where they fall in each of those two variables and you're done. Whereas in the normal enneagram system you basically have to look through all 9 types and pick the best fit. Much less efficient that way, and harder to compare the types.
Additionally, there's the wing system which is in my opinion just silly. Why would 4 and 5 be as close together as 8 and 9? They don't seem equally close to each other whatsoever. And the whole 142857 -- OMG they're the numbers you get in order when you divide any integer by 7 and look at the decimals! It's like...so what? What does 7 have to do with anything? Why two separate groupings? Why don't the arrows all follow the same pattern?
Our wing system actually makes sense, or is at least consistent with itself. You stay within one grouping and look for your second closest type. Then you do that with your other grouping. Those are your wings. Done. Each possible wing is just as close as each other one.
Basically our system gets all the good stuff from enneagram (quick typing for example) and throws away the stuff that makes no sense. The types still correspond to what you've learned, we've just provided a shortcut method to getting to them, which on top of being faster actually makes more sense.
Now that I've actually read your system, I can say I think you've done an impressive job in devising it, and I'm still trying to get my head around it.

You have indeed created an interesting theory - and I like how you have based it off the Hornevian and Harmonic groupings, as well as the Instinctual Variants. According to your system, I think I would be a 4>5>6 S-P-I, considering the following:
Social > Preservational > Intimate
Turbulent > Suppressed > Controlling
Avoiding > Anticipating > Pursuing
?
However, this is inconsistent with my understanding of how the types are present within me - I think that everyone has each of the nine 'drives' within them, it's just that one seems to take the lead as a strategy for coping with life. For me, I feel that Six and Eight are the drives which are least dominant, and that my wings (Three, Five) are the second most dominant besides Four. While the wings merely add flavour and behavioural characteristics to the personality, the points of integration/disintegration constitute the subsequent 'movement' that the personality makes, for better or worse. For example, in my 'movement' to One, I strive to improve myself and my environment for the sake of purity and rightness, I overcome my self absorption and self consciousness that results from my fear of defectiveness by aiming for what is objectively right for both myself and others. However, in the move to Two, I will overestimate my need to be loved by others, my subjectivity in regard to my perception of others will increase, and my ego will become inflated with illusions of being more important to others than I actually am.
I find the original system to be uncannily accurate, and this system you've created is not The Enneagram as the title would imply. 'Enneagram' contains 'ennea', which means nine, and 'gram', which means graph. Though you've used knowledge from the original system, it is not The Enneagram and further comparison would be detrimental to our perception of both systems. Aside from the fact that you've used information from the original, they are different systems which follow different logic.
So, if I can't convince you when it comes to The Enneagram, I guess we'll just have to agree to disagree.