The problem you are going to run into with using the thin plywood is how to join it at the corners. With thicker stock you can use rabbet joints or even butt joints and glue nails, but with 3/8" or 1/4" there isn't enough glue surface for a box that size, IMHO. The bottom will add a lot of strength, but it will still be prone to twisting which will pop the corners loose. You could add corner blocks, but that will eat away volume in the two engine compartments. Maybe just swapping the engine and plug/ignitor columns and putting the plug compartments in the corners will allow you to use corner blocks and still have enough room.
3/8" is way overkill for a box that size for that lightweight load. 1/4" is plenty for the sides. Consider 1/8" luan ply (door skin) for the dividers (or even Coroplast) and the bottom, and glue the bottom to all the dividers to keep it from bowing.
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