That looks like a good project for pocket screws so they would all be inside leaving the outside clean.,
Good glue with ply makes a pretty strong structure if the racking is controlled by the construction. You could glue 3/4 x3/4 ply pieces on the inside of some key but hidden corners. If you tacked or. P in nailed them on first, they would index the large pieces to avoid slipping when you assemble with glue.
Some of the take down hardware also does a strong job while preserving good looks. (Like the IKEA structures).