As the title suggests, the larger gaps are to be filled with Kumiko. The smaller gaps will be left empty. I though about a simple pattern as in the demo lantern on the right in this picture.
Do you have other ideas? All I can currently do with my mitre saw are square patterns. Cannot do triangles, unfortunately.
https://youtu.be/JbpwDufvzSo
This is a 90 degree shooting board. You can make one where the fence is 30 degrees and use it to ensure your angles. It's a bit slow, but so is kumiko in general.