'No one is born into the wrong body' is erasure, but so is 'trans channelers don't survive puberty', and most of the other solutions.

Having Aran gar switch to saidar doesn't work, as she would be completely unfamiliar with how it works and not be effectively able to use it without years of training. Travelling works differently and so forth. If sdhe can use it effectively, that carries unfortunate implications of its own, in that it devalues all the work channelers have to put into learning their abilities, or possibly that saidir is easier to learn or something.)

If there is any ability to switch which Source you access, then the breaking doesn't happen.