To me it seems more likely that they will soon either be caught by the knights or head towards ardumesha. Because except from finding what happened to erkin's parents, there's nothing to do in the north anymore (plotwise) and since ardumesha is the place where she got the divine favor it could also be the place where they might find a way to get rid of it somehow. (just my opinion though)
Coukd be, just acording to the old lady, there is nothing to find in Karia's myth. Sure Ardumesha will probably be involved but I since we have now established there is nothing to find in Karia's myth I doubt that will be the trigger to solve the divine favor problem.
Author could go that route like you said or he has to find another way like I was thinking by stumbling upon weird stuff surounding Elkins parents,which isnt what it seems. Imo we can both agree that author defo goes the route of hardships that eventually results in Kaya surviving(clash with knights, kaya being hated by the norterners etc)