After putting this project back on the shelf for a while I am finally getting back to it. The next order of business was to simply cut the box tops and bottoms to size. To do this I first needed to assemble (dry-fit) the boxes together. To do so you simply layout the box sides as you plan to assemble them end-to-end. Then hold each joint together using some masking tape. I'll use this same procedure later when I finally glue up the boxes. Once the sides are securely and tightly taped, I fold up the ends to for the box sides. I then close up the box and take my measurements of the interior.
As you can see on the left the zero-clearance jig allowed me to precisely set up the height and placement of the grove. I cut a grove on each side (long-side) for each of the 4 pieces for each of the 3 boxes I am making.
The key here I found was to not be too shy about cutting the groove a little deep. You don't want the lid and or bottom sliding around on you too much, but that can always be taken care of later. It's more difficult to undercut, assemble, test-fit and re-cut the grooves deeper to accommodate the top later.
On the left you see an example of how I cut the grooves in each of the box pieces. Notice that the groove for the bottom piece is 3/16" deep by 1/4" wide (the thickness of the ply-wood bottom). This results in a recessed bottom. This is different than the plans described. The plans describe cutting a locked rabbet joint which results in a flush(flat) bottom. This was an oversight on my part, but I don't mind. If anything it gives the box a bit more interesting look being a recessed bottom.
For the top groove, I cut a 1/8" wide (thickness of the saw blade) by 3/16" deep groove which is easily done without touching the set-up. This will accommodate the locking rabbet joint for the offset top piece.