For larger empires, the king should be scaled up in size. Its flat out impossible to find someone's king when they are big enough; trying to find one small icon in a empire of 10,000 towers is stupid.
#Scaling enemy King
lofty phoenix
misty sphinx
I usually find their king, and then encircle them, so that I have a hostage if they refuse to allow me to take their land, making their king larger wouldn't make it easier to find it and by the time you reach one side of the empire, they might have already moved their king somewhere way further away, so this wouldn't really change it or make it easier.