Well, here are my theories for how it might realistically play out for each of the possibe routes.
Gaston - Probably the crown will end up passing over to Cassidy's cousin, because he seems so genuinely committed to her, I doubt he would ever agree to an "arrangement" like Nazagi's. Being in love with Cassidy as he is though, I doubt he cares. All he really wants is to be with her.
Nazagi - His route is the only one that addresses the problem directly, and as we all know, his solution is to impregnate Madelleine and pass their children off as Cassidy's. It may or may not work since Madelleine and Cassidy look nothing alike though; I guess if their kids resembled Nazagi enough they could successfully fool everyone. Who knows.
Callum - Cassidy probably either ends up with Oscar or never marries at all; in either case, the crown will almost certainly end up going to Cassidy's cousin (like Gaston, Oscar isn't the type of guy who would likely agree to a "solution" like the one Nazagi comes up with). I suppose a daughter of Callum and Madelleine's could be passed off as Cassidy's if she resembled her aunt enough, though Callum and Cassidy don't resemble each other much so I think it's kind of doubtful. Plus, given how furious Callum was with the charade their parents pulled with Cassidy, and simply because this is Callum we're talking about, I doubt he'd take very kindly to such an idea. Anyone who suggested it would probably get a fierce butt kicking.
Oscar - I'm pretty sure on this route, again the crown will simply end up going to Cassidy's cousin no matter what, because again Oscar isn't the type of guy who would likely be willing to take a mistress to father children with - if he and Cassidy get together, that is. If he and Madelleine get married then I think Cassidy will simply never get married at all.
Dolores/Unaligned - Again, Cassidy most likely won't ever get married, so yet again her cousin will be her successor.