I think you're probably on the right track here, but I think your takes are on the charitable side. The Ferengi would clearly like to believe their attitude is “If you’ve got the lobes and you’ve got the Latinum, I don’t care what you do,” but in practice they are very committed to some massive societal disparities which are not financially profitable.
In a society so deeply stratified by sex (and far from egalitarian in other regards), MtF trans folks would likely be looked down upon for apparently abandoning a way of life which Ferengi males clearly consider both morally superior and far more pleasant than the lot of a woman. In practice I suspect very few would condemn themselves to the legal status of a Ferengi woman by openly transitioning. They'd seek out secret treatment, and private expression, but publicly continue to appear as men.
Conversely, FtM trans people would be viewed with intense suspicion: a conniving, cynical Ferengi would likely view such a case as a woman attempting to escape from her rightful lower place in society. Frankly, given the horrific situation Ferengi women are placed in, if FtM trans folks were accepted as men even in the minimal legal sense, I'd expect at least a few cis women to attempt to take that avenue out of the societally mandated hellhole they would otherwise be condemned to. Perhaps the Ferengi have reliable tests for gender dysphoria that would doom these efforts, or perhaps not.
As for non-binary folks, I don't think they'd get it. Either you're a normal (male) Ferengi, or you're an inferior and powerless woman. How could someone possibly fall between those two states?
In short, the incredibly pervasive and legally enforced sexism of Ferengi society creates significant complications for trans folks of any kind. It's a really horrible and frankly depressing setup, which the Ferengi themselves are willfully oblivious to.
Post Rom, I would expect the women's liberation movement to be a watershed event for trans folks of all sorts, and lead to a fairly rapid normalization of Ferengi publicly being their true selves. It's still going to be a rough road socially, but clearing the legal barriers will go a long ways.