The Asur would 100% take one of their own, disgraced or not, as their queen over an Eonir monarch.
With Fanriel, there is no doubt that she is loyal to Ulthuan, the concerns with her are over her personal judgement and ability to fulfill the duties of the station appropriately. With Marrisith, first of all you'd have to get her to accept, and if she refuses that is an incredible humiliation for Ulthuan for extending the offer only to get turned down. Even if she accepts, she lives in Tor Lithanel and is Queen of the Eonir, would she give those up to move to Avelorn? Probably not. Even if she does accept and move to Avelorn, can the Asur trust her to have the best interests of the Asur and Ulthuan at heart, rather than exploiting them to the benefit of the Eonir, or just taking revenge for the actions of Caledor II and Caradryel?
With Fanriel it would remain an internal matter, with Marrisith it becomes a matter of geopolitics and foreign policy. And Fanriel is a closer relation, her bloodline diverged from the Everqueens much more recently than Marrisith's.
Like, I'm not saying that any of this is even remotely plausible, but if it somehow came down to either Fanriel or Marrisith as the next Everqueen, and if the Asur had a choice in the matter (the process of selecting the next Everqueen is not exactly a national referendum), they would take Fanriel.