Edmund,
A spline could still be used as long as it wasn't glued along its full length. Were it to be glued at one end say , or in the middle with a glued portion of length less than say 4 inches, you should be OK. However, as noted in the link Wizer provided for breadboard ends, the relative movement is then discernible.
Personally I wouldn't bother at all with a spline. If you alternate the boards forming the top (rings on board ends alternating up and down), then any cupping of individual boards, cancels out to a degree (albeit creating a washboard effect in the extreme).
Quartersawn wood is far more stable than flatsawn stock and will not cup worth a mention, although it's true there is QS and then there is "real QS". The latter is a very wasteful cut and only worth doing on big trees so you won't find it unless you buy the tree and pay to have it cut that way. Still even what passes for QS these days won't cup to any degree.
Not all woods look good quartersawn. Unless it's like oak with medullary rays, it can look very plain. For oak it is the traditional cut for Mission (USA) and Arts and Crafts furniture. Your shelves belong in the latter category although the example you show is not in fact quartersawn.
The quality of wood available to us today is vastly inferior to that that was around 100 or 150 years ago. There is a lovely book called "The Wheelwright's Shop" (
http://tinyurl.com/e2qcs ) that tells how the strength of oak and elm so diminished at the turn of the century, that pieces formerly made of wood, now had to be made of iron.
When you think of how to fix the table top, you must also bear wood movement in mind and not fix the top so that movement across the grain is blocked. Search here and elsewhere for mention of eg "buttons" to help deal with this.
