(2/2 -- sorry for the novel -- this is a big subject and difficult to be both concise and accurate about)
Plus mtf is much more fitting as we have been treated like men before we began transitioning and to varying extents adopted those social rolls.
Odd that you would go out of your way to point out that sex and gender are not the same, and then claim that a sex-based terminology best represents a gendered experience. Going by your explanation of social roles, MtF/FtM is totally inadequate, and MtW/WtM (man to woman and woman to man) would be more accurate. But MtF and FtM are admittedly the terms people know, so even if technically inaccurate their preexisting presence in the lexicon may make them better than MtW and WtM. As for how they compare to my suggested list, once again, that's a matter for each person to decide for themselves, of what terminology is most accurate to their own experience. If you find MtF truest to you then that's likely the best term for you.
Lastly our biological features aren't intrinsically gendered. Those of us binary trans folk which pass still experience gendered violence (or the lack of) when transitioning, something which I have personally experienced. Saying that the body of someone who is transitioning it's still what they started with when they experience otherwise it's just wrong.
The body of a person who transitions (particularly when talking about HRT and with things like retraining your socialization and patterns of speech) does become a body of the gender they're transitioning to, true. People see us as the gender we transition to, and we experience the same treatment as other people seen as that gender. But from a medical perspective, we don't leave the sex we were before transition. Our primary sex characteristics are, at most, cosmetically altered but not literally changed in sex in terms of tissue makeup. Whatever genetics we have are unaltered. Bone structure may be cosmetically altered in some areas, and if not yet set may become somewhere in between our birth sex and the sex we transition towards, but doesn't fully change over. Biochemistry comes closer to a full transition, but we still don't fully replicate the hormonal cycles of the sex we transition towards. Secondary sex characteristics where there is no correlate for the opposite sex (such as breasts and facial hair) may be removed, so this is really the only aspect where more of a full change is currently achievable. I do believe (based on admittedly limited research, so we'll see if this bears out with further study) that neurobiological sex characteristics are a thing, so a trans woman is likely female-brained and a trans man likely male-brained in full. I suspect, though this is unevidenced, that people who desire non-binary medical transitions may have neurological sex characteristics which are intersex. But other than that, almost every other sexual characteristic of trans peoples' bodies continues to bear some stamp of the sex characteristics they were born with. With advanced enough prosthesis (maybe aided by gene therapy) it's possible that we will be able to fully transition peoples' primary sex characteristics as well, and fully transition their biochemical makeup (probably related to ovarian/testicular prosthesis) but even then marks of the sex at birth will remain a part of the body -- trans bodies will remain in a middle-ground best described as transition from an invisible intersexedness (the mismatch between neurology and anatomy) to a synthetic anatomical intersexedness which brings them closer to resolving the brain-anatomy mismatch. Short of literal full transfer of the electroconsciousness into a clone altered to be another sex, complete sex transition is a fiction.
Gender isn't simple but biological essentialism is not the answer. So many people are left behind and the experiences of so many more after just invalidated.
Simplistic biological essentialism is certainly not the answer, and gender is a social construct defined by choice (albeit a choice usually based on essential internal truths) and independent of biology, but I think beyond that we disagree. Boiling everything down to a feeling about gender, without questioning the origins of that feeling, in my opinion, is what leaves people behind, as well as stunting research. There is some evidence of sex characteristics of the brain, which could go a long way in explaining body dysphoria, as well as related points like why some intersex people desire medical transition and why others do not. And of course when it comes to measuring neurology we have to be careful not to be too deterministic -- factors of socialization and choice play just as important a role in why people feel the way they do about themselves as neurobiology does -- but anatomical sex characteristics beyond neurology are certainly inherent, and the evidence tentatively suggests that at least some elements of our relationships to those sex characteristics are also inherent to our neurobiology.