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I wouldn't think quartersawn is relevant to this. No matter how the log has been sawn, the length (or height) of the boards will come from the length of the trunk, and when wood shrinks it doesn't shrink significantly in that direction. The shrinkage and swelling is radial, i.e. the trunk gets fatter and slimmer, which will translate into the width or thickness of the board, as opposed to the length. Again, no matter how it was sawn.
You see this is log cabins, which when properly built allow for the logs to slip and move to accomodate the shrinking widths as they age and get thinner, although the lengths of them does not change.
The big difference in "laminated" wood would be if you were using veneer-cut (rotary cut) wood, which is used to make plywood. Much more stable because the wood is literally sliced from the log the way you "peel" paper from a roll, and then the plies are glued alternately cross each other to counter any movement. If you were building up laminates from thin sawed boards though, you'd still be working with boards, not veneer cut.