Make the sliders that fit into the dovetail grooves.
Make 32 of these as shown in the diagram. They are 2½" long and their cross-section dimensions match the grooves. One half of each slider should be a snug fit into a groove (where it will be glued), and the other half just slightly loose so that is slides easily through the groove of the adjoining rail. I find that a bit of sanding is enough to do the job.
Hint: make half of these sliders just a little bit longer than the others, maybe 1/8". This will make final assembly much easier when the time comes.