It is really interesting food for thought Brad!
I guess I look at even temperament as a sort of platonic ideal/truth, since it is highly functional, and then adjustment of fine tuning for given intervals in a composition as an incidental point...a sort of "fudge factor" to be adjusted to taste for the scenario.
I think if I tried to intellectualize 57 possible notes within C, it is just too overwhelming. I suppose practice makes perfect, and thought processes like that can just become a natural habit. I admire your delving so deeply into this issue.
On a different note... in that video example, when it shifts to "justonic" for some of the examples towards the end, wow does it sound weird! Initially, striking me as out of tune, I guess because of expectation. I bet it wouldn't sound as weird if it was a string instrument of some sort.