While examining the CD case, I found the case itself has a little trim feature along the corners. I ended up drawing a profile that included this feature in Fusion 360. A straight piece I test printed went on a CD case with a satisfying snap. All the joints are extrusions of this profile.
I realized during assembly that the joints need cutouts where the trim pieces interfere with the extruded profile. Nonetheless, I was able to get the whole house assembled only needing to reprint 1 piece. However, there are one or two that might be a little stressed because of the force required to insert the CD's. If I where to build another of these, I would model the CD case in Fusion 360 and remove interfering material. I think that would make the whole thing easier to assemble.
I printed it in Taulman Bridge nylon, which is stronger but more flexible than PLA. (I learned about nylon filament during the boy's science fair project, but that is a different story.) Everyone is happy with the final result.