Cut sliding dovetail pins on the ends of each drawer divider, using a router with a dovetail bit and a shop-made jig.

 

Before installing the dividers, I cut two mortises in each the divider's rear faces to accept floating tenons milled on one end of each of the drawer runners. I left the drawer dividers unglued so that I could slide them out when screwing the top in place. This gave me access to the inside of the drawer bay to drill and screw the top on. With that done the dividers were glued in place.