I’ve been picking away at pieces of the router plane box and finally glued in the last bracket (the one for the fence) yesterday:

I took off the clamp today and did a test-fit of the tools:

That went surprisingly well. Both planes fit in there with no problems; I have room for a few more blades as well as the small router plane (if I ever get it). I could also fit the miniature router plane inside.
During this project, I also added a wooden lining to the fence. It’s the same privet that I used for the new mallet, which should be fairly hard-wearing.
For whatever reason, I made a lid consisting of a frame and a floating shiplapped panel. After gluing that up, I cut a rabbet along the bottom so that it can fit onto the top of the box:

After trimming the dovetails and such, I had a finished box:

Or rather, I had a complete, unfinished box. I normally leave shop projects unfinished, but for whatever reason, I decided that I wanted to apply tung oil to this thing. That turned out to be a messy affair, because I couldn’t get the cap of the bottle open, pried it off, and ended up splattering some of it around. Oh well, the bench now has a slight oil reapplication.
That takes some time to cure, but at least I don’t have to do anything else. Time to move on to the next thing. And no, it will not be a box for my plow plane, tempting as that may be.