There were several qualities and thicknesses of plywood available. Modifying the Sketchup model to adapt for changing plywood thickness was really error-prone and annoying.

Using the measurements from the Sketchup model, I calculated the area of the sides of the cabinet and backbox. It came out to 1.86 m² by treating the sides as rectangles.

Finally I settled for a fair grade of pine plywood, 10 mm thick, 2m x 1 m for 498 kr (€53) at Fredells.

I used Inkscape to make a plan for how to fit the various pieces onto the plywood, and how to have the lumberyard cut the sheet (red lines) with as few cuts as possible (they charged for each cut, I ended up paying 100 kr (€11) for the cuts:

Unfortunately it turned out that the lumberyard could only cut all the way across the sheet, so I had to do some quick improvisations.

Finally, I had my pieces: