I thought about the rounds splitting and I found a way, but never took the time to try it.
With a thin blade like a bandsaw, you cut the round in 2, 3 or more parts, then let it dry gently. Most of the shrinkage will occur freely, widening the cuts, but not by increasing the internal tensions (much less at least). Now, cut again at the previous cuts to eat the excess of wood in the middle, not touching the bark. Cut many times, keeping the kerf's sides parallel, until the outsides of the different parts meet again each other. Smooth the sides nicely, and glue back together the parts. The reconstituted round shouldn't move now, excepted if the ambient humidity changes drastically (don't drop it in the pool).
Is that clear or muddy?