If you feel you need to bricklay and pattern-rout stacked layers in order to get an accurate curve I suggest keeping the thickness down and use 3 or 4 layers as trimming with a long router bit invites chatter. Saw as close to the line as possible. You may get some router tearout near the joints due to grain direction reversal and you will have a busy looking assembly. For exterior use reinforcing the endgrain joints with dominos and epoxy is a good idea.

Bricklaying will give a somewhat stronger result than full height segments. Veneering over the bricklaid assembly will strengthen the back further. You will have to decide if the extra work is worth it. The original makers kept it simple and I would do the same, segmenting the curve in full height pieces with splined and epoxied joints, then sawing and sanding.

The strip laminated approach can work, you need thicker cauls and more clamping force.