Given how the Masadans are written you'd pretty much would have had to rewrite Manticore having a Queen to give that even a chance of happening and even then, I'd suspect they would try to horrid things to Honor who'd almost certainly would have been sent by people trying to send her to her death.
You underestimate the power of Manticoran realpolitik and Masadan fanaticism.
Masada is evil and insane, not stupid. They know that Haven does not share their ideas about the Proper Place of women. They're willing to make an alliance because they want Grayson's World, and that means they need Haven's support. Politics ain't beanbag.
If Haven was lucky enough to get Grayson- clearly the superior ally- then Manticore would be left with Masada. Of course, David Weber writes Manticore as Good People who are fundamentally unwilling to do Bad Things. They would never ever make a deal with a horrible regime for a fleet base!
The best way for David Weber to write Manticore is simply to make politics a minor background detail. Let Honor have fun adventures in space, and use the Star Kingdom as flavor. Tell the story of Space Adventures, the fight against wicked pirates and scheming Havenites, and ignore the Manticoran goverment. This is the right way to handle a good space opera.
The second-best approach- the one I adopted- is to just accept that politics ain't beanbag. Like most nations, the Star Kingdom struggles with ethics in foreign policy at the best of times. When faced with a long-term existential threat, they will make any treaties necessary to protect their people.
Even if Manticore was a happy egalitarian democracy, foreigners are not their constituents. They do not care about Bad Things happening to other people far away; they care about Bad Things happening to them.
Again, why do you think it matters if they're technically mobile? The only reason to go with a first-rate, second-rate etc system is vibe and treating your shore battery/sea forts expy as first-rate warships ruins that. And if 'the vibe is dead' as you claim, why in the world would you try to change to a rate based system at all! The only reason to use such a system in your space scifi is vibe!
The system of ship classification is an absolutely meaningless detail. If the characters and the plot are good, the vast majority of readers will not care. If the characters and the plot are not good, then you have bigger problems.
Weber plays around with Age of Sail, but he's not willing to really commit to it. If you want that kind of vibe, check out Drake's RCN series.