Responding to questions + clarifications of fact in the game world:
It can be a good idea not to provoke powerful people even if you don't depend on them for support. You've met 2 Tilean nobles; you can probably imagine how they'd behave if something similar happened to a daughter of theirs.
Vendetta is a fun word to say.
Maybe not super relevant to the discussion, but I would say anyone who said this IC would not be giving an impartial account.
Maybe more relevant: most of the men who made up Alvarr and Rorik's armies are still around. Very few fighting forces suffered anything close to 100% losses in the war; the Iron Company are formidable but there are definitely enough fighting men/women and weapons in the Reaches to challenge them.
If by an army for hire you mean a pre-organised force, then yes, they're not that - but a pre-organised force is going to come with a pre-organised leader. I'm guessing what you guys are discussing here isn't just how to send an invitation to Sforza v2.
Similar to the statement about Belehir, I'd say someone who said this IC was picking a side. Carraciolo is second-in-command of the Iron Company and Lord-Lieutenant of the North, but Sforza has made no explicit moves to place him above Valdes in any kind of hierarchy, or to tie him to the succession. He hasn't got noble blood. The practical reality than in the event of a contested succession he'd have the most men is pretty much the only claim he'd have.
Put another way - for Carraciolo to get any real legitimacy beyond might makes right, Sforza would have to acknowledge the possibility that he and Irene could die childless.
Responding to the general discussion: I think you guys know where you each stand on this (barring Bardhyl of course). There's no immediate IC decision to be made, just Ludo gathering information - so I think the thing I would think about is not just where your character would stand, but what they would do with their knowledge of what the others are thinking. Intra-party tension can make for some fun moments, but mainly when resolved through actions rather than reiterated in words. Maybe you have other ways to solve each other's problems, or ideas to alleviate each others' fears - if you do, it would be better to think about those now, when your fellow PCs have raised the issue, than later when those problems have already happened.
I've redrafted this bit a silly number of times, because I don't want to push you guys in any particular direction or show favour to any particular IC argument, so I won't say any more. I'm not encouraging you to split the party - I think we probably had enough of that with Adelbert the spy - just encouraging you to think about how you can address what all the PCs want, rather than just individuals.