Make up an adjustable jig similar to this one http://www.nationalwoodworkersclub.c...ustom_edge.jpg
This jig cuts the banding from the top in plane with the base of the router using a flat bottomed bit.
Adjust the router bit so it cuts the edging just proud of the plywood surface and take down to flush with your sander.
Might have to modify the edge guide to allow for that “square” cut edge at the wide side of the box where the bit would need to be lowered down for a side cut (similar to a normal flush trim cut)
I think I would add an auxiliary handle to the long side of the jig just to keep the thing steady.