John K Jordan
What kind of wood? I have a Woodmizer and have cut and air dried slabs from a variety of trees. (I haven't made a natural edged slab table though.) I find some like walnut and eastern red cedar are easy to dry flat and stay flat. Others, like oak and persimmon and sometimes cherry - not so much if at all.
I assume you will try to cut through the widest part of the log to get a wide slab, avoiding the pith. This should help some since it will be nearly quartersawn. How far to get away from the pith is a good question which also may depend on the wood itself. I understand some people would cut through the pith, rip down the middle to remove the pith, then glue the halves together. If the grain is straight in the center the seam might be invisible.
That said, if I wanted to make a slab table I would consider slabbing it thicker than needed (anchor seal the ends), sticker and air dry to EMC, bring into a conditioned space for additional drying, then flatten before use. (Seal both sides equally, of course!) This even works for persimmon!