Very reasonable analysis; thank you.
Where biological differences are relevant, they should be reflected in law and policy, but where they aren't, then transgender people should indeed be treated as the gender that they self-identify as.
Would be interesting how Jewish law would apply in a case where a Jewish transgender woman would carry a pregnancy to term once that will become possible. Would the kids automatically become Jewish, or would it depend on who produced the egg? What if the egg was produced from her own (male) genes through in-vitro gametogenesis, as is likely to eventually become possible? Then would her kids be Jewish?