The Tzitz Eliezer is at the end of Vol 10 25:26:6. The teshuvah discusses transplants, and he raises the question posed here as a hypothetical. A second teshuvah, in vol 11 #78, is about someone with a hormonal issue impacting their sexual development during gestation who is born looking female, but has one testicle. In both cases he says that gender is decided by external organs, not internal ones.
I frankly do not know of anyone else who wrote on the topic. Also, notably, REW wrote a teshuvah, i.e. intending to be follows in practice -- lehalakhah ulema'aseh, as opposed to R Bleich's more theoretical journal article.
Speaking theoretically, I could see logic of a third position.... That with regard to halachic gender differences based on role, the person's gender is that of their birth. So that the person in question would still be obligated to wear tefillin, daven three times a day, etc... But when it comes to gender issues related to sexuality, their gender is their new assigned gender. After all, if the person is now female, is yichud with men or with women more problematic? What to do about minyan, which is interpersonal but not sexual, is beyond the scope of my speculation.