I will start with good things:

And I thank you kindly for them.

The musical interludes were cute once and annoying ever after. I stopped reading them.

I can see that. I started using them in imitation of other Chessverse stories, but I may have started going overboard.

The chess games are even worse; perhaps that's only because I don't care about chess, but even so that limits the audience sharply for those passages.

I tried using as much banter and kibitzing during the games as I could, to try to keep the reader both interested and with a good idea of what was going on. I'm probably going to end up deciding it was a mostly-failed experiment, and not go into quite so much detail of a particular game in the future, unless there's an actual pressing plot-point depending on the actual details.

I'm puzzled by the way the fic handles gender identity.

Star Chaser is treated the same way, with some limited interest in being changed back but with female pronouns in the narration and so on. I don't understand what you're trying to say about gender/the sex change magic/these characters/etc.

Since the point where Star Chaser got an actual name, I'm trying to write her as 'trying to do the right thing' - which, at the moment, means she's working with problems that have somewhat higher priority than her gender. If Celestia happens to pass by, Star will be entirely willing to give her Missy's letter of recommendation and ask to be male again. I'm not aiming for this to be so much about the unimportance of gender, but of how important existential risks are compared to everything else.

The fic is written from first-person perspective, from Missy's point of view. At the moment, she sees Star Chaser as female, so those are the pronouns she's using to refer to her.

The romance rings false throughout.

This has, in fact, been in my road map for a while - and I hit hard on this point, on almost a metafictional level, in the latest chapter. I hope it passes your muster for dealing with the whole issue in an interesting and entertaining way.

You write things out of chronological order by dropping into the pluperfect ("I had taken a clever precaution earlier"; "I'd already thought of that"; "I'd given my enormous offscreen staff that task the previous week", etc.). You do this conspicuously and very often. This ruins real peril (maybe she'll just pull another pluperfect solution out of her rear), makes it harder to understand complex series of gambits (wait she did what when?), and puts a lot of emphasis on some of her less plausible memories/resources/allies that you'd do better to tuck into corners. Having her work through problems forwards is also important for the aims of a rationalist fanfic: you can follow the thought process as it goes. The pluperfect cheats at that.

This is something I hadn't even realized I was doing so much - thank you for bringing it to my attention. I'll try working on improving at this, though I may not always succeed as well as I should.

You're doing a lot of "bringing Earth science to Equestria" and also a lot of "doing the generalized scientific method to magic". They're in tension, worldbuilding-wise; be careful.

I'm in regular communication with some of the major authors of the setting, in which various aspects of the worldbuilding are hammered out. Eg, if someone wants there to be a magical mineral with certain properties, I'll point out, "but if you mix it with this, then kaboom". A few hard limits have been placed - nobody's going to be building any nukes (or equivalents), though MOABs are a possibility.

You are juggling a lot of stuff, and you're not putting it into tidy, episodic plot arcs, either. Science! Politics! Training up the assistants in rationality! Magic! Travel! Tacked-on romance! Cameos for canon favorites! Greek deities! Other "game pieces" who you won't put out of their misery by letting them find out Missy was human too but who keep running around in the background! Jail time! Engineering! Diplomacy! Pop culture references! Collecting new friends! Extortion! Dueling! Archaeology! Spontaneous musical theater! Chess! Dependents of the lovedrunk and puppy variety! It's very busy, you're resisting wrapping up any of the plots you open, and it's dizzying. Perhaps this is an element of realism you care about; but it's in tension with the (Watsonian) realism of "there are only so many hours in a day and memories in a head for Missy to be doing all of this" and the (Doylist) realism of "I can only juggle so much content in a single story".

Given what I know about my writing from other instances - I do seem to have a greater tendency to open up new plot ideas than to tie them off neatly. If it helps, I do have a roadmap of where I plan on taking the overall story, with various highlights and items I want to hit on the way. (How many words I spend getting to any particular point is, however, an open question.)