finally updating this with some more thoughts, mainly prompted by this post from @butchhamlet! (And there are some other great thoughts about trans readings of this play here!)
[Beatrice is] an unmarried woman dependent upon the hospitality of her uncle. This is the same position that Rosalind in As You Like It occupies at the court of her uncle, Duke Frederick, but there marriage is not the constant topic of conversation—and, of course, Rosalind manages to make her escape, together with her cousin Celia. In Much Ado About Nothing Beatrice and Hero are the young women of the household, and it is expected that they will marry.
[...]
Beatrice is not an heiress [...and] her position is more precarious than Hero's. [...This] will return, more vividly and painfully, after the humiliation of Hero, when Beatrice longs to revenge her cousin and must instead enlist Benedick's aid to fight with Claudio: "O God that I were a man! I would eat his heart in the market place" (4.1.303-304). It is worth noting that in other Shakespearean comedies of this period the heroine does become a man, at least for a little while. Portia, Rosalind, and Viola all cross-dress, assuming male costumes and names in order to perform some act of rescue, release, or revenge. But Beatrice has this option only in the wishful form of a condition contrary to fact. Much Ado About Nothing is a play that engages topics like male bonding and female disempowerment, for all the powerful figures in Messina are men.
—Marjorie Garber, Shakespeare After All
This is such a great point because women disguising themselves as men is such a hallmark of Shakespeare's comedies! And this is a play about, in many ways, the various masks we wear--and yet Beatrice's desire to hold the position of a man (power) is the subject of a tragic and impassioned speech rather than a lark of crossdressing. In Much Ado, that gender boundary is utterly impassible; which sets us up in a very interesting way for a trans reading.
Because in this reading, Beatrice DID transcend that divide, which is exactly why she can't do it again. The pressure for her to perform femininity is all the higher because she has to "prove" and "earn" her place as a woman. She doesn't get to masquerade as a man and have a funny little adventure. Her being brash and outspoken is already pushing it.
Or, to look at it from the other direction: Beatrice already spent half her life dressed up as a man, pretending to be one. The play is now set in a time where, narratively, that opportunity has passed. That plot arc has already happened. That trick won't work a second time.
I think there is a parallel to Lady Macbeth here--another woman begging a man to do violence for her. But in Macbeth that desire is largely selfish, while in Much Ado it is to serve the protection of another woman. So often in Shakespeare, it is the women who get shit done, who take things into their own hands (sometimes, but not always, via crossdressing) so when a woman can't do that it feels significant and intentional. Beatrice is such a strong character and yet still helpless in the face of gendered power dynamics.
Masculinity in Much Ado is also very linked to credibility, which is another reason the ol' crossdress maneuver wouldn't work. It's not just about gendered power dynamics, but also class. Who outranks who? Who has had favor conferred upon them by a prince? Who has their masculinity revoked for being too young or too old or too dumb?
We see this perhaps most keenly in Act 5 scene 1. First, a confrontation between Leonato and Antonio vs Pedro and Claudio. Antonio is enraged and questions their masculinity, calling them cowards and pale imitations of men for their actions against Hero; when they leave and Benedick arrives, Claudio jokes about how "two old men without teeth" tried to fight them.
And then Benedick rebuffs their attempts at joking around and issues his challenge to Claudio. Immediately they seek to undermine his masculinity. Claudio is like "isn't it wild how he's questioning my masculinity lol" and Pedro launches into a made-up story about Beatrice talking shit about him, including innuendo about her saying Bene has a small dick. Knowing that Benedick is in love with her, they tease him about getting cucked (which, in fairness, he talked about at length earlier in the play). Benedick's parting words refer to Claudio as "lord lackbeard" which is definitely a reference to his youth and probably also implying he's too young to be a "real" man. At no point do Claudio and Pedro take this seriously; this confrontation becomes less about Hero and more about dick-measuring. Indeed, the reason Claudio is so incensed to begin with is that Hero cucking him is an insult to his (extremely fragile) masculinity. By punishing her so spectacularly, he is re-establishing his credibility as a man.
(This is also why I tend to read John as trans--despite his rank, he is an outsider and his masculinity doesn't "count" the same way everyone else's seems to.)
There's definitely more here, but I'm still chewing on it.