I'd warrant there's a lot more than 3 ways of doing this. I can think of at least 3 more ways. I think you should avoid making such limited, absolute statements as it undermines your argument somewhat.
I don't really think there are any more ways to change a characters gender. You can have a woman occupy the role of a character that used to be a man.
For instance Captain Janeway occupies the same role as men like Picard and Kirk, and similarly there have been female descendants of characters like Robin Hood, who may call themselves Robin Hood, as its become a title by this point.
That however is not the same thing, and neither are female distaff counterparts like say, Supergirl, She Hulk, and Batgirl.
In terms of actually changing a characters gender, the only other way I can conceive is if its a body snatcher thing like Brainiac or the Demons in Supernatural, but again that doesn't work for the Doctor as he obviously is not a body snatcher. Also its hard to have a hero steal someones b body.
You could maybe do a Freaky Friday type body swap between the Doctor and his companion. I wouldn't mind that for one story. Might even be good fun, but I don't see that working long term.
If you had the Doctor body swap with a human female, then it obviously couldn't last as she would be a human. If you body swapped him with a female Time Lord however, the same problems still arise in that now the character is permanently female, in which case you've kind of changed him too much. Added to that now that he has been changed into a woman against his will, then he will never be as comfortable as he was as a man.
Also to be honest body swapping people between genders can lead to gender politics taking over stories which is always sh*t. And yes I feel that goes both ways. Look at the Blake's 7 episode Power that's utter sh*t, the worst episode of the series by far. War between the sexes or a writer moaning about how one sex has it harder should be kept out of sci fi IMO at all costs.
I'll be kind and assume your latter examples contain a soupçon of comic exaggeration in order to hammer home your analogy. The Doctor (in spite of his new-found Lothario status) has been atypical in terms of the type of masculinity he's portrayed to the audience over the years. Indeed, he's been the antithesis of 'toxic masculinity' i.e. non-reactionary, very little interest in sex, peaceable and using force (only) as a last resort, so the jump to a mildly androgynous female incarnation doesn't strike me as extreme a leap as , say, Lalla Ward to Jason Statham or Arnold Schwarzenegger.
Actually my comments whilst meant to be funny are not that big an exaggeration.
You see the thing that f*cks me off about all this is the way people say "the Doctor can be anyone, so why not a woman?" That's the thing though, he can't be anyone!
The Doctors core personality always remains the same. He always enjoys travelling, he always prefers non violent solutions, but will kill if need be, he hates being told what to do, and he is always mysterious too. Even physically there is a template to his character. They all tend to dress in Edwardian/Victorian era clothing, tend to wear hats, and tend to have big, long, or messy hair.
Its just the outer personality that changes. Tom Baker said this in the Docu "Whose Doctor Who" that the role was the most limited he had ever played as there were so many things he couldn't do as then he wouldn't be the Doctor anymore, whilst Terrance Dicks said the most important thing to do was not change his personality too much. JNT even made all 3 of his actors grow their hair out to resemble the first 4.
So many people however refuse to acknowledge that there is any similarity between the Doctors, so I bring up Brian Blessed as Susan, and Vinnie Jones as Romana to show that actually the Doctor, and therefore the Time Lords don't just completely, 100 percent change when they regenerate with no similarity to their predecessor.
If there are absolutely no similarities between incarnations of any Time Lord character, and all change is good (which is the crap the female Doctor advocates push) and Time Lords have no concept of gender at all, then yes. Brian Blessed is as legitimate a choice for Susan as say Morven Christie (who I think would have been an amazing choice for Susan.)
The second you say "oh no Brian Blessed is too silly to be taken seriously as Susan", then you've admitted that I am right that there is a template to Susan's character, as Brian obviously doesn't fit within it. So does this not apply to the Doctor?
So now that we have established that there IS a template to Time Lord characters why is it so outrageous to assume gender is a part of that? Gender is a huge part of everybody's personality. And yes that applies to trans people, hence why they change!
Now okay the Doctor is an alien, but even then his gender has still become a part of his overall template. Really the only way it couldn't be would be if they had deliberately written the Doctor as gender neutral for years, but they never did.
All of his relationships have been written from a male perspective. He's been a grandfather, a father, a husband, a boyfriend, he and Jamie were very much like two brothers, he and the Brig clashed as two alpha males etc. Also all of the actors who played him brought aspects of their male personalities to the role, he always dressed in male clothes etc.
To say that the Doctor wasn't a masculine character just because he wasn't macho or obsessed with sex IMO is short sighted. Sherlock Holmes for instance is very much a masculine character, but he's not interested in sex, and he's not macho.
Meanwhile there are plenty of female characters who ARE macho and obsessed with sex. Look at Xena. Compare her to Sherlock Holmes. She f*cks anything that moves, and is the ultimate badass. You couldn't get a more feminine hero than Xena.
The Doctor was also inspired and created in the mould of the eccentric, Victorian, Edwardian, British gentlemanly hero. The somewhat pompous, patriarchal, yet loving grandfatherly figure. He's a mix mash of Sherlock Holmes, Bernard Quatermass, H. G Wells and Jules Verne. Even physically you can see this in the character with his bohemian hair, frock coats, penchant for funny hats and wild dress sense.
A woman therefore sticks out like a sore thumb. No matter what woman you cast. Obviously yes some women are better choices than other women, same way some men would be better choices than other men for Susan. A young, skinny, nerdy guy for instance would obviously be better for Susan than Brian Blessed.
However that's the point, said man isn't going to be as good as Morven Christie or another Susan type woman, because gender is a part of Susan's character too. So why not just go for Morven Christie, or another woman who will flow better? Same applies to the Doctor.
Changing the Doctors sex, especially after 50 plus years, completely shatters the illusion that the Doctors are all the same man. I look at the image of all the Doctors with a woman tacked on and I think "why is that woman standing there after all those guys" It looks out of place.
But it's an interesting logical assertion that you're happy for another Timelord to change gender with a justifiable narrative explanation, yet an absolutist when it comes to the Doctor. Indeed it's possible to extrapolate your logic to any Time Lord in the show given the right narrative justification. After all, there aren't 'just' 3 ways for a Time Lord to change gender, as your argument for the Master's gender change amply demonstrates in spite of yourself.
The Master is not just another Time Lord however. The reason it works for the Master is that he is established as being a body snatcher. Even then however you couldn't just write him as having stolen a woman's body and not care, as he is still a male character, and still a misogynist.
However with a proper story justification then yes the Master could work (though even then its a relatively pointless endeavour as we still have the Rani, who is a great villain, screaming out for a rematch.)
Again with the Doctor there is no proper story reason to change gender. Retconning that he was always gender neutral makes 0 sense, and changes the character too much. Having him suddenly become transexual because he hates being a man is stupid too and in danger of trivialising gender dysphoria.
So all we are left with is a Freaky Friday style swap, which as I have said is really only good for short term. Maybe you could stretch it out for a couple of episodes at the most, but even then it would come across as a gimmick. So the question is why go down this minefield?
