Turn the table upside down and set a 1x4-inch scrap board inside the table frame, lined up with one of the long 1-1/2-inch square dowels. Run a bead of glue along the side of a medium 1/2-inch square dowel. Place the dowel on top of the 1x4-inch scrap board, with the glue side to the table frame. Secure in place with a nail gun.
Repeat on the second long side in the same manner. Continue with the shorter 13-inch sides using the small 1/2-inch square dowels. Repeat this process on the bottom tier of the table, clamping a longer board in place to set the 1x4-inch as a guide.