Put a small amount of glue on the dowel, drive it home, and you get a very strong connection without metal fasteners.
The chamfer for the handle on each end can be as simple as a bevel made with a handplane.
The handles go outside the recessed ends. The recessed ends look cool, and also provide a bit of room so the nails or dowels won't split out the ends of the sides.
These top pieces tie the sides and ends together and retain the sliding lid.
With the case assembled but the bottom not on yet, place the lid in position with one end just clear of the top . . .
. . . then trace the other end with a pencil. That gives you the location of the outside edge of the opposite cleat.
With the cleats in position on the lid, trace the ends of the z-brace. This is easier than trying to calculate the length and angle!
Here's the sliding lid in the shut position. Slide it to the right, and:
Now the lid clears the top, so you can simply . . .
. . . lift the lid out of the box.
The cleats are wider than the lid, so they rest on the sides of the box and keep the lid from falling in. Note: it's not obvious in these pictures, but the bottom of the box is below the sides, rather than captured inside them. This is the traditional approach for this type of box. I think it has to do both with preventing water from wicking up inside (these are jobsite boxes, remember), and so that the bottom rather than the sides takes the wear when the box is pushed along the floor (or ground).