Something I just noticed about the Stones of 3 certain towers:

White-Gold: The Amulet of Kings is the spirit of st. Alessia
Red Mountain: The Heart of Lorkhan is the beating heart of a "dead" god
Walk-Brass: The Mantella is a soulgem that contains the soul of either Zurin, Hjalti, or Wulharth (unless the Dwemer are the actual stone)

I'm not sure about the other Towers and their stones, but these three have a common theme being that each stone is part of a once living thing. If that's the case for all the towers then what could the stones be for them?

The dwemer did not become the stone of Walk-Brass. They became Walk-Brass. The Dwemer are the tower.

Then what's the stone?

Was going to be Shor's heart, but likely it's the Mantella now. Maybe Tiber's Totem.