Tried to scrub the Apple ][+ lid with basic dishwashing Sunlight and brush, worked quite nicely. This plastic is heavy and seem to attach itself lot of black stuff wich came out very easily with this solution. Let's see how the whole case turns out.
Precisely because the case is painted, you should take care in how you wash the case.
Very likely you have now very small pinholes all around the case from air bubbles that popped through the paint. Check very closely. They are little black spots.