Thank you so much for bringing up this topic, Ayya! In fact, the very issue of the legal implications of ordaining transgender persons is what I want to focus on in my graduate studies. So, it might be sufficient to say that this kind of Vinaya exploration is my ‘jam.’
I don’t know in practice whether or not a transgender person could be ordained, I suppose it very much depends on whether or not one view transgenderism as fulfilling the category of paṇḍaka, of which Ajahn Thanissaro references in point one that you’ve quoted.
The five types of paṇḍaka are:
…those who are born as either neuters or sexually indeterminate, those who have lost their sexual organ or capacities due to circumstances after birth, those whose sexuality changes every half month (in some versions from male to female and back again), those whose sexuality depends on the initiation of others (or, in another version, having oral sex), and those whose sexuality is engaged by voyeurism. 
In Sanskrit and Pali these are :
I think it would be very legally difficult legally to determine whether or not transgender persons fit into the category of paṇḍaka, because there really appears to not have been an equatable gender orientation during the time of the Buddha. Dr. Gyatso makes the point that “…this third-sex pandaka category, rather than being consistently or coherently defined, is starting to look more than anything like merely a loose catchall for an ever-expanding array of sexual aberrations on ever-shifting grounds—even psychological and social ones” . Thus, the term paṇḍaka was used to categorize people who were sexually or anatomically different, particularly when compared to the stereotypical non-deviant male.
Which is why I always sort of feel icky when the example that Nicolas has quoted is brought up, because though very interesting, it’s not an example of transgenderism. Because of course one who is transgender does not just wake up one morning as the opposite sex; and furthermore, if the monk in that story showed signs of sexual or anatomical changes before his ordination, he might not have been able to ordain in the first place. So it’s difficult to tell if transgenderism should fit into the category of paṇḍaka. I’m not sure what monks these days have determined, but I would think that one would have to join whatever order (bhikkhu or bhikkhuni) they identify with. I’ve heard that at a certain monastery (that shall not be named) they ask transgender individuals to stop their gender reassignment surgeries and revert back to their birth sex, which makes me want to throw up.
Oops, I’m ranting. I hope at least some of this is helpful.
Also, let me know if you want me to send you the cited sources. They’re excellent reads and Gyatso gives fantastically detailed examples of what “sexually indeterminate” means.
P.S. It makes me very happy that at the top of the Wikipedia page for Paṇḍaka it says,
 Janet Gyatso, “One Plus One Makes Three: Buddhist Gender, Monasticism, and the Law of the Non-excluded Middle,” History of Religions 43, 2 (2003), 96-97.
 Leonard Zwilling, “Homosexuality as Seen in Indian Buddhist Texts,” in Buddhism, Sexuality, and Gender, ed. Jose Cabezon (Albany: State University of New York Press, 1992), 204.
 Janet Gyatso, “One Plus One Makes Three: Buddhist Gender, Monasticism, and the Law of the Non-excluded Middle,” 107.