After asking my friend Chuck lakin for an "oven consultation," not only did he come over to consult, but offered to cut my plywood in his shop. What could I say? Normally, I simply cut plywood with my skill saw, but it's a lot easier and more accurate with a table saw.
My initial reaction so far is that maybe the structure is too monolithic, but to get lots of mass and insulation really does take some space. When the oven is complete, I think it will look a lot better.
What's next? Now I can fill the cavity between the masonry and plywood with cellulose insulation and cover the top with a metal roof. After that, I'll constrict the size of the oven opening, create an overhanging tongue and do something about the dreadful, naked plywood look.