Exactly like you, I would like to begin by saying that I have no animosity nor prejudice against anyone. What I am saying below is not meant to be offensive to anyone, it is just an honest account of what the data in my region says.
"I can only think of 2 possible solutions ... either a difference in
psychological predisposition between the sexes (but if so what), or
some genetic component."
But there is in fact a third factor, which is economics.
Where I live (Southeast Asia), there's quite a large number of many male -> female trans people that are prostitutes. I have lived in Indonesia, Philippines, and Thailand, which are all countries that appear lower than 80th in the list of countries by GDP per capita, and do have a large population of people living in poverty. If you go to the streets where most of the prostitutes advertise themselves (such as Jalan Jaksa in Jakarta, Indonesia) you will find these days that many of them (and in some areas, the majority of them!) are male -> female trans.
This may get quite controversial, so once again, I begin by saying that I have no animosity nor prejudice against anyone. I just want to point out, if I may, that for men, it is not as easy to make money as a prostitute as it is for women. Men statistically pay for sex more often than women do. I have not seen any homeless women in my city acting as "beggers" (I only see men doing this), but I see far more female prostitutes (in fact I have never in my life seen a male prostitute advertising themselves on a street!). Most of the trans-women I know in my city, started out as pre-operation trans people that made ends meet as escorts or prostitutes or "sugar babies" and many of them got the money for their operation by a "sugar daddy" or a wealthy client that developed a closer relationship with them.
I am not saying this is the only reason. I am just saying that there is at least one more reason in addition to the two that you have suggested as the only two you could think of. What I have written applies to my region of the world and may not apply to wealthier places such as Luxembourg where practically everyone (even the poorest people) are better off than the middle class here (and would less likely need to resort to prostitution).
It is also likely that the answer to the question depends heavily on the region in question, as is the case for sexual orientation demographics.
Let me start with the opening sentence to the Wikipedia article on "Demographics of Sexual Orientation":
"The demographics of sexual orientation vary significantly, and
estimates for the LGBT population are subject to controversy and
For example, the same page has this:
It shows that males are more likely to be gay than females in every city in Brazil except for Manaus which is in the Amazon. We cannot rule out the possibility that in Manaus, there might be cultural or societal reasons why 10% of the women have become attracted to women more than the men. I am not saying that the men of Manaus are bad people, I am just saying that genetics and psychology are not the only factors and that culture and society can affect what type of people a population finds attractive (in a misogynistic society women might start to find men less appealing, for example, so it is not just genetics and psychology).
Interestingly, in USA the statistics are the opposite of in Brazil (women are more likely to be gay than men):
I suspect that just as the demographics of LGBT people "vary significantly, and estimates for the LGBT population are subject to controversy and ensuing debates", the same may be true for trans people (in fact trans is the T in LGBT, so already there's at least one other place that says that statistics will vary significantly and be hard to generalize).
I am not saying that psychology and genetics don't play any role at all, but I do think we also have to consider other factors that would lead to more males becoming trans than females such as geography (are we in a place where it's acceptable for men to transform but not women? are we in a place where more women are in demand for certain jobs? are we in a place where more women are in demand for sex?) and in some cases even economy. Because of this added complication (which gets into "soft" sciences of sociology and economics which are harder describe in a more mathematical or clinical manner than "hard" sciences like neurology), it might be very difficult to get a straight answer regarding psychology and genetics, especially since all the data is also relatively new and people haven't been studying the topic for long enough yet!