I know that my hands were white after I cleaned the bottom half of the case, and the Wikipedia on isopropyl alcohol says that it removes the plasticizers on vinyl records, so I know that isopropyl is strong: I've never used Simple Green (and read some reports that it also removes plasticizers to a degree).
I've almost decided to use denture tablets for the top half of the case since they did a good job on the keys. I'll try to soak up to just below the labels. The case is relatively new (1996) and not that dirty; it's just a psychological thing that I want to get rid of the previous user's body oils and lotions and such. I'll consider spot-treating with isopropyl, though perhaps I'll dilute it (most varieties are 70%, but there's a Meijer store brand variety that is 99%).