The wood base seems to be made from two pieces of wood--the "floor" and the "walls." I would guess that the stone is glued to the floor so it reaches down to the seam between those two pieces of wood. It is likely to be a fairly substantial stone. From its apparent age, I agree with Jimmy that its likely to be a natural combo.
I'd try the dry heat first so that you can save the base. Once you get it out, you could put a shim down inside of the base to elevate the hone up higher. This would allow you to use both sides of the hone while still maintaining the antique appearance and functional use of the base.