Actually the problem with alternating the boards to prevent cupping is the exposed surface looks like crap, no hope of grain matching . The exposed surface looks like a piece of cheap furniture in my opinion .
As far as i am concerned I grain match the boards on and job that I can tie down [say a table top to the apron]. Sometimes I will also do the same for free surfaces . In this case I might take several weeks to get the surface to final thickness, making adjustments each time I machine the surface until the surface can sit for a few days at least and remain stable . Between each machining surfaces should be stacked so that air can get to both sides . When stabilized apply the same finishing treatment to both sides and with a little luck the thing will stay flat.
One solution to the alternating board theory is to cross veneer then veneer lengthwise to the original boards..........mjh