I know you're all just dying to know how this is going...

I had decided not to do any more touchups on the cabinet, but when I had my best friend over the first thing she said when she saw the machine was "Wow, the wood is really torn up." Well, it's only damaged along the bottom of the backbox really. The box looks like it got water damaged at some point; the plywood was delaminating, the top layer of ply had chipped off along the bottom, and the ply was warped with paint misssing at the top of the box. The damage wasn't as bad as it looked, but of course with chunks of paint missing it really drew the eye.
In an earlier episide I had glued and clamped the wood back into submission, but this still left the missing chunks of ply. I finally went at it with PlasticWood to fill it in, sanded the heck out of it, and re-painted. (Unfortunately, sanding lightened up some of the green paint when I wasn't careful, but I think trying to fix it without an airbrush would look worse than leaving it alone.)
The results aren't perfect, especially the repainted red part of the curtain image, but it at least doesn't leap out at you now.