Shutting the Moot down, which made some sense from Lucan's point of view
at the time, was a serious long-term mistake on his/his faction's part.
It immediately cast the legitimacy of his claim into doubt.
...
Oh, I'm not claiming [Margaret] would have a chance in the short term. In the long
term, however, (and she/her faction were playing a long game right from
the start), she was the clear best choice. She had a claim by blood,
she'd have had a proven record of good governance by the time the dust
started to settle, and would probably have been the strongest faction
standing.
If Lucan had had a lick of sense he'd have simply ignored Margaret, and
once Dulinor and Strephon were out of the way offered her an Arch-Duchy
with even more self-governance than was customary before the war. Then
marry one of her daughters or something.
Hmmm ... I'm not sold on the wisdom, or not, of Lucan proroguing or dissolving the Moot; I'm open to convincing one way or another here. Better a dissolved Moot than a Moot that is going to be implacably hostile, not only to Lucan, but to the forces that he was figurehead for. (Which in turn suggests that the "Lucan" faction was composed mostly of military figures, and did not have a particularly strong influence in the Moot.)
Definitely he needs to put any potentially legitimate candidates for the Throne under lock and key. It is not Margaret (the individual) he needs to neutralise, it is the "Margaret" faction at court (and the "Dulinor" faction too, though they are going to be keeping a very low profile!). Buying off, or ignoring, an individual would not prevent that individual from becoming a figurehead for opposition factions - see Theodosius III.
Lucan's (and "Lucan's") greatest advantage was the strength of his personal claim to the Throne. That advantage was compounded by making sure that no other candidate remained with even a passing personal claim. With Margaret out of the picture, opponents would have to go back at least 3 or 4 generations to find a legitimate alternative to Lucan. We are speaking Henry VII-level dodgy claims to the throne here.
And once there are no legitimate options, the only alternative for opponents of Lucan is a dynastic change. Then every Archduke or head of a Great House is in with a shot ... which means that really, none of them do.
Lucan could have been the most noble and gentle soul in the Imperium. Still, his hold on the Throne is going to be much more secure once Margaret has an "accident".
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Cheers,