Hey Kelly!
Nice article...and the earlier review too!
I think if I were going to try to really define harmolodics, I'd have to do some framework-level pespective sifting first.
One basic given would have to be that, whatever it is, harmolodics is likely to have evolved over time, and so cannot be reduced to Ornette Coleman's version of it.
More importantly--and this dimension is explored pretty interestingly, methinks, in David Lee's book on the "Battle for the Five Spot" --it may be that musical theory may not be the best interpretive framework for understanding harmolodics, or at least not the only one.
Lee situates Ornette Coleman's harmolodics socio-historically, and interprets it through the lense of Bourdieu. Because I have similar training--and am pretty much a moron when it comes to music theory--I find this kind of answer very compelling. Along the same (-ish) lines, I really like the framework for understanding modernism in Afro-American jazz that is laid out by Griffen and Washington in their book on "cool" (see my sig). If you ask them "what was harmolodics?, they'd say that it was, in part, a particular, and particularly important, Afro-American performance of masculinity, one which existed in a fraught, dialogical relationship with white notions of manhood and, as well, competing Afro-American ones, in this case profoundly embodied in figures like John Lewis and the other members of the MJQ...and of course Miles Davis.
I'd also probably want to start with the idea that, whatever it is, harmolodics is fundamentally a kind of praxis--i.e. a form of revolutonary action informed by theory. This would also lead to a heavily contextualized kind of definition.
Thanks for asking this!
I think it's always interesting to acknowledge that in the question, "What is X?," the meaning of "is" is not unequivocal!
PS I'll trade a Sinatra doing "Lonely Woman" for a Hegel singing "My Way" LOL