If you only have a jig saw, once the rectangular frame is made, lay it on the plywood and trace out the exact dimensions of your front/rear panels, then cut as close, but OUTSIDE, the lines as possible, to avoid excess sanding. The 4 Pi Pro's I built in this manner were all plain glued butt joints, done with care. I think leaving out the screws joining the panel edges MIGHT reduce the chance of splitting later, since stress at the screw holes is avoided. For sure you save the time otherwise spent drilling/screwing and applying filler over the heads.

For a single project, the "drill/glue/screw method" will be cheaper than buying the 6 clamps or so I needed. Be sure to invest in the proper pilot hole drill for the screws you choose. Good Luck! Sam