We always edged the cabinets after they were assembled. If you are doing very many it would be worth getting an underscribe router attachment. With that attachment you would cover the sides of the cabinet first and then do the shelves letting the strip overhang the joint about 1/16". Then you use the underscribe router to trim the laminate to length and it makes a perfect seam.
I made my shop cabinets out of 3/4" melamine with butt joints and PB screws. I edged them with the iron on type before assembly. I used a $10 trimmer that is sold next to the edge banding. For my needs (a few cabinets), this method worked well.
This may not work as well for you because of all the dadoes. You'd have to be careful not to catch the trimmer in the dadoes.
I ended up edging them complete. I used a hobby knife to trim the edging. They came out alright. I will invest in a edge trimmer if I ever decide to make anything else using this material. Thanks for all of your help guys!
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