I could ride the body of the grooving plane on the outer edge of the bottom, and then adjust the iron so it was protruding something like 5/16" (8mm). The finish of the groove isn't superb, but it doesn't have to be.
After making the groove I dry assembled my parts: Sides, ends and the bottom.
Inside it looks just like I had envisioned. But on the outside there is a bit of a gap. I still haven't made up my mind if I should add a small piece of wood to act as a moulding, or if I should just leave it the way it is.
My problem with adding some moulding is that it will disturb my design idea of the rounded outer edge of the bottom to look like a piece of moulding in itself.
I didn't plan for movement on purpose, but the bottom is able to move just a bit in the groove which is good news.
Wood movement is mostly limited to expansion after being worked out here, so being a little bit loose is not a problem.
My plan was to continue on the lid, but I had to make a slight alteration in those plans, as our refrigeration compressor started acting up.
It has been giving us problems for the last couple of years, and we haven't really been able to pinpoint the fault.
After fiddling with the compressor, I just managed to saw some stock for the lid, before it was time to make an evening round and stop for today.
Test assembly showing the small gap.
Close up of the interlocking parts.