Maybe this?
It's only 6 layers, not the 7 I got the previous way, but thanks to advice from @nervous_jesse I'm much more confident it'll hold together.
Each layer is 7 pieces, but adjacent layers are cut at alternating corners so there are overlaps. There are holes for dowels at each of the corners, to hold it all together.

Now I need to work out how to buy some plywood and get it into the makerspace, or ask for another one from their stock.

#BeachSpectres