Getting read to start ripping the ply for my bookcase project first thing in the morning. Don't have my dado set here yet, so I couldn't assemble even if I rushed this one.
Have you considered doing dadoes with a router?
When I go to glue up the carcasses, I'm faced with slow downs due to only having 3 bar clamps. Would nails hold hardwood ply tight enough for glue up with through dadoes? I had planed to shoot 16g 1-1/2" approximately 12" apart, but can shoot up to 2-1/2".
When I started out, I had no compressor, so all my mechanical fastening was done with my choices of...finish nails, screws, trim screws, or box nails (if not seen). A well fitted panel in a dado with glue and nailed...and allowed to dry makes for a good joint. If you want the nails totally hidden, you could go to the trouble of "blind nailing".
For finished ends that have been fastened with a 16ga, or an 18ga, doing all your finishing, and then just using a fill crayon renders the hole pretty much invisible.
If you only clamp up opposing dadoes three clamps should seat the fit, even for 24" cabinet panels. For 3/4" stock, a 1/4" deep, by 3/4" wide dado is all that's necessary. You also might consider making up some pipe clamps in 1/2" and 3/4". For well fitted dadoes, a 1/2" pipe clamp up to 5' is more than adequate to clamp. If you are bending the pipe, make a better joint. Good fitting joints don't need that much clamping force. Pipe clamps are fairly cheap.