One could ask, "what is this mess?" While they may look messy, these items are the components of the worlds oldest clamping system, which is known informally as "sticks, rope and wedges". This system dates to the Romans and for the purpose of gluing the two thin halves of the top together it is the best!
The reason it works so well is that as tension is applied to bring the two halves together, equal force is applied to keep them flat and parallel. The result is a truly perfect system that can only be improved upon by updating the materials. Shown above is a picture of the clamp in action, where hot hide glue has been applied to the joint. I use hot hide glue wherever feasible because it works so well. It is one of the strongest glues available and creates a thin joint.