The softened diagonal lines indicate that the edges art not coplanar and to create the surface, additional edges are required. That comes down to fundamental geometry. In the plywood for your climbing structures, you could induce a bit of twist to compensate. Not in SketchUp however.
Follow Push/Pull from Joint Push/Pull Interactive would thicken the geometry and provide the miters along the seams.
Screenshot - 8_17_2018 , 5_03_29 AM.png
You would still need to make each panel a group or component. I would make them components with Replace Selection with Component turned off. That will allow you to use the miter faces and edges in each neighboring component. You'll have the components in the In Model library to drag out so you can lay them out for nesting.
Your profile indicates you are using SketchUp Make but you need to be using SketchUp Pro for this work.