I don't think it works under rationalism (conceptually) either, to complete the yin and yang here.
Philosophically you cannot combine gnostic dualism* (the belief the body is a prison and the "real me" is beyond it, meaning the body doesn't matter), with a materialist outlook that the body must be altered to be "the real one" or correct gender in this case.
I don't believe anyone can accurately capture what it truly means feelings-wise to "be a man" or "be a woman". That's to say without relating to their sex organs, body, experiences, ect. There is no internal measurement of either without looking into social expectations and experiences. So to hear a transgender person describe themselves as "internally, I am a man/woman" always sounds farcical.
Troonism simply depends on unravelling so much we're left with almost no meaning at all. We have to go ridiculously far backward into questions of "what is form?" As you said, it's an intentional usage of spaghetti code.
*Gnostic dualism was proposed by Satan to Adam and Eve in Genesis 3:4. Interesting coincidence, but not my overall point.
This is where the trans movement is really losing itself with overreach.
Again, trying to be a charitable as possible, if someone were to tell me that they have an obsessive disorder to present as the opposite sex, flouting normal social convention, I would say "okay". Maybe there's better treatments for it, but in terms of harm, a dude wearing a dress, or a woman dressing as a man, is either minimal or non-existent. Some people might be uncomfortable for a while, but styles change all the time and people would get used to it being a possibility. Given what we know of obsessive disorders already, the idea that someone could develop one related to gender presentation makes sense. There are plenty of obsessive compulsive issues the operate on a social/interactive level, so it's inline with the other diagnoses of the kind. Though I would note here, presenting as the opposite gender would really be a coping strategy more than it would be a cure, but people playing with gender presentation is a big part of the gay community, so for me, it's no big deal.
(Also, as a side note, if you look at the few studies that have been done on Body Dysmorphic disorders, suicidal ideation is at 80%, and attempts are at 25-30%, so the idea that suicidal distress is somehow unique to trans experiences is incorrect. If anything, it seems like it makes it more likely that gender dysphoria is a subtype of BDD.)
This is my personal opinion on it, it's not necessarily the right one, but I'm coming at it from trying to be as accommodating as possible to difference when there's no harm to it.
But obviously, the problem then becomes that framing it as a disability disempowers the trans person from making their own choices (especially in regards to invasive surgeries), or at the very least puts in place the possibility of gatekeeping, which many trans activists seemingly want to avoid. It also implies that this is an accommodation society is doing, and hence could be subject to reasonable limits, like limiting access to women's spaces. And yeah I think "philosophical spaghetti code" is the best way to describe it, because you having laid out this way, they are essentially claiming the existence of some sort of soul or a separate inner self. But if they were come out and state that, then that's staking ground on a claim more in the line of spirituality than science, which would make their claim of uncontestable truth impossible to maintain. So they have imply that interpretation, while never committing to it.
I don't know if anybody watched the Philosophytube (British dude who explains basic philosophy concepts, often poorly in my opinion) video on transphobia, but I remember someone linked it to me, and it was really sloppy in the way a lot of this argumentation is. He was making the argument that trans people are placed in an impossible situation of having to argue their own existence, which isn't correct. I am not denying that a trans person is experiencing distress from their self perceived mismatch, I am saying that the meaning of that distress (and from that, the best course of action to alleviate it) are not what the trans person claims. In the same way I do not deny the existence of a schizophrenic person, even if I deny that the voices they claim to hear are actually separate entities communicating to them.
So yeah, in a way it seems like the trans community (or rather trans activists) is trying to do a run around the concept of truth to avoid having to actually argue about how to interpret their experiences.
