Ed, IIRC, he resaws it fat. As you noted, going directly to the final thickness off a resaw is asking for trouble. My impression was that resawing off opposite sides of a thicker board is a recipe for more manageable results than simply resawing thinner stock in half. He still would take proper care with the resulting boards, bring them down to final dimension in stages, all that good stuff.
And since this is still wood, I’m not sure how quartersawn is going to help you. If the problem here is immediate movement after resawing thinner boards from thicker stock, then moisture and tension can still exist regardless of the grain orientation, so I’d be concerned that you’d be spending money for no real gain. If instead your concern was wood movement due to seasonal changes, then sure, quartersawn boards will move much less than flat-sawn boards. Hopefully I’m not misunderstanding!