I got lost somewhere in the middle of your description somewhere about here:
Then cut the walnut into strips to make end grain strips the same thickness as the maple square.
These will be glued onto the perimeter of the walnut. This will be long grain to long grain.
Could you add a sketch.
I don't think it would make any difference if the thickness was 3" with a 2" bowl or 2" with a 1" bowl.