You should try adding little supports between the squares and the rest of the bottom layer. And cut those away after print with a knife.
Like it's done on popular print-in-place iris box design (https://cdn.thingiverse.com/renders/f8/2a/86/20/03/632f221f5ecd05ef6f8ae306d77ccba4_preview_featured.jpg).
Any 3D editor should be enough to add this. I'll do this myself and publish a remix if mine won't print :D