To decide whether someone has “moved across the gender divide” we need a definition of “gender.” If we take the simplistic external definition, then it seems that some people can move across that divide, since that’s what sexual reassignment surgery does (which is, as you probably know, a good deal more complex than amputation-and-implants)
BTW, man so reassigned is probably a low risk of being a rapist/bathroom danger :)
But, it seems you reject that interpretation out of hand, just as does about everyone — we’re coming to see “gender” as an “enormously complex” mix of biological and social constructs, almost too subtle to pin down. And if that’s so, then it’s useless (or at best, pedantic) to focus on whether a given procedure constitutes “moving across the gender divide” because there really isn’t a “divide” so much as a continuum.
The important thing is to step back from obsessing over this currently-vague and “enormously complex” distinction, and just see that some people are in real pain over the way they feel in their body. Then the question to focus on is whether some treatment (surgery, medication, psychotherapy … whatever) can help alleviate that pain and let them be happy and productive members of our culture.