Again - I'm going to offer up using a lock miter bit.
#1 - the lock miter bit removes the finish - along with the wood - and leaves nothing but a glueable surface.Two problems:
1) I don't know if the pre-finished plywood will take glue. I suspect it won't.
2) These things have no joinery elements; they just fit together theoretically on paper. It looks like a difficult glue-up to get them to form a 5"-tall box with smooth sides. See the gaps in the photo.
#2 - Lock miter joints are among the most simple to glue. You just tape and roll.
The downside of course is the hell you go through setting one up. That can easily be done though with the use of special tools that make it easy to do.