I'll admit I'm not much of a hand tool guy but I would approach it the same way as I do when using my open sided planer/molder to make raised panels. It does a great job on long straight grain but can blow out the corners of end grain. My solution is to either glue panels together so they are very wide or add sacrificial pieces to each side to make the ends, then rip the panels to width and then mould the sides. So in your case I would work the end grain of a wide board to the profile you want and then rip the lid to width and then mould the sides. Working with the lid with wide boards makes control of the plane easier because more of the sole is contacting wood. It is more difficult to work on the end of a 3" wide board than one that is 10" wide. The upside is that you have partially made material for future boxes.
Pete