I made a new type of box with a sliding lid made of flex:

This first prototype is a bit stiff as I used coarser settings for the flex of the lid. The hope was the lid would be  a bit more robust. Now the generator uses a setting in between that works just fine if the sliding surfaces are treated with wax. Rubbing a candle on the left and right most part of the lid does the job. I also sanded the front edges of the lid so they don't get caught on ridges along the track.

The inner corner is not made with flex but multiple straight pieces connected with non orthogonal finger joints.

This is a bit more robust as it is in part the inner bottom of the box.

I also added another variant in which the lid continues around the second top corner, too. Sorry, no good pictures yet.