>Cut plywood for the bottom to 21 3/8" by about 4 feet long.
With 1 1/2" sides, this would be correct. With 3/4" wood it would be 19 7/8".
> Glue & screw a 2x10 "box" onto this plywood.
If you do glue it (and I wouldn't for the bottom) remember it will be a bathtub if you don't put some drain holes in it. Make the drain holes 1/8".
> Inside dimensions of the box are then 9 1/4" deep, 18 3/8" wide, and about 4 feet long. If I DON'T rabbet the upper sidewalls and just rest the Langstroth deep frame top boards on the 2x10 side walls, it leaves 8 11/16" of the frame hanging in the box. That will give me a bottom space of about 9/16" (9 1/4" of the 2x10 minus 8 11/16" frame). Then finish the project by cutting another piece of plywood for a top with the front top board pushed back 3/8" to give it a top entrance and ventilation. What am I missing?
If you are using Hoffman frames, cut two sides to block the gaps between the frames. They should be 1 1/8" wide, by 3/4" tall by four feet long. Probably put one at the back as well and leave out the one in the front or add the entrance to the cover to prop that up enough to let them out.
>Now, I'm planning on cutting and using my own typical TBH top boards, but I think having the flexibility to use standard Langstroth deep frames from nucs or splitting other deep Langstroth type hives is easier to incorporate now as I'm building the TTBH as opposed to adapting it after it's built.
Assuming you are not using very many hoffman frames, you could just make a small block for each end for when you put a frame in, I suppose, but I'd rather just have it covered so I could mix them anyway I see fit.