That's fairly unlikely, given that the Broken Crown is the name of the royal crown of Saldaea. As Perrin has a connection to it, I doubt Jordan would confuse matters by having the viewing refer to the crown of a vanished kingdom.

As Jim said, Perrin has officially given up on Manetheren and seems to intend to keep his word. Not only that, but he's negotiated a very public and official deal with Elayne and can't turn the TR into an independant Kingdom any time soon without forcing Elayne to declare war on him.

It's fairly late into "the last book". The mood of the moment is to form large political alliances that are "permanent", in the sense that they're not only to fight TG (if they will survive afterward is another question...). It long seemed like Jordan was grooming Perrin to become a neo-Hawkwing but 2/3 into AMOL (the end of TOM) he unveiled his plot twist and it now seems that it's Elayne he intended to form a kind of empire or federation (and eventually this will require some resolution vs the Seanchan - war or treaties etc. ). It seems to mean in the third Age, the Dragon's friend leads the AS, one of the Dragon's wives will be the central political ruler, and it makes it sounds likely that Aviendha rather than Rand will soon take the role of the leading figure of the Aiel as the Car'a'carn's wife (we should have seen this coming earlier, there was ample foreshadowing from Sevanna's ambitions of the power the WO who marries the Chief of chiefs will wield....). And then, Rand already announced he doesn't intend to be the Light's "general", which opens the door for Mat. LTT was forced to wear too many hats... military ruler, leader of the AS, he seems to have gained some political role above the regional rulers during the War of Shadow (possibly to coordinate the war effort), and though that is still mysterious, there is his tie to the Da'shain who were called Children of the Dragon. It sounds like this time around, Rand/LTT intends to devote himself completely to being the Creator's Champion, leaving the other responsabilities to others.