Well, I have a way, it seems a little tedious, but it will work to generate all the parts for CNC.
Three cabinets. One produces the sides and top and top two shelves, its bottom is DO NOT CUT material (DNC).
The second cabinet has its top specified to be the same size as the bottom of cab 1, and it has a stretcher tight to its bottom side with my desired lock tenon joinery. This cab only cuts the top part, with the other parts DNC.
The third cabinet is for getting the under-bottom stretcher part for cab 1. It is wider by 1.5 inches, and has a stretcher up against the top with lock tenon joinery, the end offsets specified so the part will mate with the part gotten from cab 2. As with cab 2, the one part is all that gets cut, the others are all DNC.
I will carefully check those parts from cabs 1 and 2 in the part editor, to assure myself the cuts are right for making the desired joint.
While I usually am not always the best at catching all the details on the first go, I believe you could make this much easier using the Std Base Frameless cabinet. Delete the back, set your toe kick height to the height of the bottom vertical piece, set cabinet dimensions, add your shelves, on the toe kick tab set the inset so it centers or wherever it needs to locate, change the apply toe kick notch to None, on the left and right ends give them a bottom inset of the toe kick height. You can also modify the toe kick's left and right insets to get the overlap you're looking for on the bottom vertical. I believe that should get you what you want.
I have a very similar piece I use in cabinets. I've attached the file. It's a drawer I made. Most of the parts are made on the CNC when cutting drawer box parts. The adjustable shelves are made the old fashion way, tablesaw.