I really like the idea of borrowing some concepts from the English Civil War to map out the proposed Third Marik Civil War. Sorry so late to the party, but I do know me some English Civil War, even if I'm not a huge Marik stanboy.
The three factions presented here don't neatly map onto the English Civil War, but there might be some parallels. The "True Mariks" seem like the closest thing to a Royalist faction -- the "provinces" that are being offered greater autonomy for support seem to refer to the large duchies and principalities, led by powerful aristocracy, rather than the independent world/provinces that are a closer fit to the 40-shilling freeholders that make up the bulk of the English House of Commons back in the day. The utter lack of outside support is...a bit odd, given that you'd expect that major trading partners would probably prefer that Sun-Tzu Liao NOT have control over two Houses and the manufacturing power of the FWL. An obvious parallel here is the War of Spanish Succession, and how all of Europe more or less unified to prevent Louis 14 from gaining (at least direct) control of the Spanish throne. At the very least, I would expect a little covert aid from the FedCom, with the Fox and trying to put his meaty thumb on the scale here, much like the French were trying to help out covertly in the ECW. That said, I love that Paul and Corinne, who play starring roles in the Jihad, are showing up very, very early here in the same anti-Thomas (now anti-Isis) role. And this suggests that Kristen's Krushers are due for an appearance with some divided loyalties -- support her baby cousin Corinne, or support her baby niece Isis?
Also, I recall that one significant plot point in the Jihad is that Corinne is vaguely anti-Resolution 288, in support of her cousin Alys who is VOCALLY anti-288, to the point that the FWL kicks her out after the Jihad and "gifts" her to the Republic of the Sphere. Granted, Alys is all of 11 years old in 3052, but still.... Intrigue!
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The Liao-Mariks are probably my favorite of the three factions in concept, but I've two concerns about the specific details. First, I don't know that this is the ideal name for the faction -- highlighting how your bitter Spinward rival is undertaking a soft takeover of the FWL seems like a poor PR strategy, especially after everyone in the Inner Sphere has had a long time to be well and truly sick of Max and Romano and their insane hijinks. How about the "Concord", because the engagement between Isis and Sun-Tzu was an attempt to revive the Concord of Kapetyn? What's more, the religious concept of a Concord is synonymous with a Convenant, which with their overt WOB support and the obvious influence of the Capellans, is what I think is the obvious parallel in the English Civil War -- this is the Covenanter faction, only more powerful than in actual history, with loftier goals. I am really rooting for Isis, because she's in the canon fiction she is forced into the "hapless damsel" role over and over again (= poor damn writing by nearly 100% testosterone-addled authors), and a massive litany of PTSD-inducing trauma is forced on her, over and over again. And her "happy ending" in the canon is getting hitched to Victor Steiner Davion as the BACKUP princess, after the Asian princess gets fridged. Ugh. So much ugh.
I do like the notion that the Capellans are not overtly helping, but rather hiring lots of mercenaries through cut-outs to assist Isis, and that she doesn't have a lot of native support in the FWL. Again, matches a lot of the Covenanter background. And it would be entirely in Sun-Tzu's nature to play the other factions against each other - "help" the Parliamentarians (Periphery Mariks) against the Royalists (True Mariks) to try to weaken both, then give the True Marik leader Corinne refuge after she is in danger of being captured by the Parliamentarians (like with Charlies 1 -- I'm revising your proposed timeline a little here, but it's flexible), and then finally trying to place the 'true heir' (in this case Isis) on the throne after Corinne is displaced or made un-alive.
If you're incorporating "The Master" (Thomas Marik the Wobbly fanatic) in the Civil War, then he has an obvious reason to support his actual living child, and turn her into a puppet to support his WOB goals.
That said, the second (and bigger) issue I have with the fluff is -- "Cult of Isis terrorists"? Seems a bit tone-deaf, not to mention I don't see the in-universe logic (Isis is very clearly a complete nothingburger and only 18 years old in 3052, with no Thuggee Cult equivalent like Kali Liao), particularly if she's being backed by the Wobblies, who would be perfectly happy to do this sort of nonsense themselves, without needing to create a front group like the "Cult of Isis".
What about bringing Kali into the mix as a wild-card instead? She's newly inherited control of the Thuggee Cult and Sun Tzu is trying to deflect any potential damage away from the Confederation by pointing his baby sister and her fanatic assassins at Andurien or Oriente on the border regions -- who also are conveniently supporting opposition factions in the Civil War.
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The Duchy of Andurien, though clearly not a major player in this Civil War, can play the Irish Confederacy in this mix-up (also not a major player in the ECW). They'd be reluctant allies of the "True Mariks" (Royalists) -- offering their aid in exchange for greater regional autonomy and regaining direct control over the Defenders of Andurien (now FW Legionnaires). You could even call the reformed Andurien military units the Andurien Rangers (as per the Jihad). They would be utterly opposed to the "Concord" (Convenaters, your Liao-Mariks), who are -- as you've explained -- in a soft alliance with the Magistracy of Canopus to split up pieces of the Duchy to "return" to the Canopians in exchange for their aid. They'd also be set up to oppose to the Periphery Mariks, who would be the obvious Parliamentarians in this scenario, set on reunifying the FWL and stripping power away from the powerful larger provincial leaders (like the Humphreys).
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The Periphery Mariks are an interesting faction. Might I suggest an even bolder plot-twist as to your protagonist Jeffrey Byrd Marik's background? What if he wasn't Martin's son, but Anton's? And that a paranoid Janos had whisked him away and claimed him as his own grandson as a safeguard against one of his own children 'betraying' him like his beloved younger brother had? Or as some twisted form of repentance for having caused his beloved brother's death? Etc. Like Ice Hellion said in the post previous: Anton's Ghost!
At any rate, as the successful periphery merchant, he can clearly play the Oliver Cromwell character in this drama, with broad appeal to the dozens of independent world/provinces that are eager to weaken the larger duchies and provinces, and curtail the power of the Captain-General by ending Resolution 288. Even better if his wife's name is Elizabeth Byrd (or even Bourchier if you're being super obvious), and she's the reason that Jeffrey had the connections and networks to become a successful periphery merchant. And if he's already a member of the FWL Parliament, and has been for quite a few years at this point -- since 3028 or 3030 or so at least (this would match Cromwell's long career in the Commons, and his years of connections that put him in position to become Lord Protector) -- and that this is where he has his political power-base and his reputation as a radical. That sets the stage for his role as the head of the Parliamentarian faction -- and gives a clear set of reasons why the Andurien Humphreys would be in opposition to him (as the Irish Confeds were to the Parliamentarians in the ECW) -- they were already political opponents for years, even decades, in the FWL Parliament.
I think without some established method (like above) for having built his own power-base, or without some major (living) power broker supporting him, it doesn't make sense for Jeffrey Byrd Marik to just hop out of the bushes and argue for his candidacy. After all, Janos had a LOT of kids and grandkids, and all of them would have just as strong a claim as Jeffrey, because the Captain-Generalcy might be dynastic, but very clearly isn't a system of primogeniture.
With the backing of most of the independent world/provinces, and maybe a few of the smaller multi-world provinces, Jeffrey would have a pretty heavy-hitting power base that should seriously concern the other claimants. He also wouldn't need much outside support (not that he'd be likely if, like Cromwell, he's promising to take power away from the major provinces, unify the breakaway regions of the state, and push through his radical political agenda).
All that's missing is some radical religious belief that is driving Jeffrey to do all this, comparable to the Puritan faith of Cromwell. What about something like a revived One Star faith? I don't know if this is a good match given that it's a Lyran cult, but something similar in the FWL (like I said, I'm not a FWL stanboy so I'm not sure what is comparable). What about a splinter Exituri sect (again, fast-forwarding Jihad plotlines and "Interstellar Players" plots by several decades)? This would give the Wobblies two potential claimants to the FWL throne!