Eowyn Vs Arwen

[The Squatter of Amon Rûdh]

Regarding possibility 3 listed above, I think that Arwen had woven his banner with the insignia of the Kings long before the War of the Ring ever started.

This is a fair comment. On further reflection, by the time that Aragorn meets Éowyn, the banner is finished and probably on its way to meet him. However, as soon as Elladan and Elrohir, who were travelling with Halbarad's company, realised what was going on I think that there might well have been trouble: I expect that they'd simply have taken it straight back to Rivendell with them, which leaves my assumption about the result largely unchanged.

Arwen was also about the only person he could have married to reestablish the Royal House as it was of old Gondor, strong-blooded and long-lived.

It's funny that this should be really: normally genealogies like that of Aragorn's family turn out all sorts of genetic abnormalities; yet in the case of the Dúnedain the paucity of familial branches is taken to be a source of strength. Perhaps Elven blood is clear of inherited defects.