Sometimes, those stabilizer inserts can act "sticky". This usually seems to happen after I've taken it out and reseated it, and the "depth" of the stabilizer is wrong, in some fashion.
Removing and reseating it again usually fixes the issue.
In your case, it's possible some crap is still in the stabilizer insert itself. Pull it out, and thoroughly clean it (inside and out), and clean the stabilizer stem on the shift key. Just make sure you pay attention to the orientation of the insert, so you can put it back properly.
Hopefully that takes care of the issue. But given that the actual switch works fine with another key, I would lay money on the stabilizer being the issue.
Oh, and in terms of denture cleaner: it's probably the best and easiest way to remove grime and filth from keys. After all, it's designed to sanitize fake teeth, which have all kinds of nasty gunk on them. Just think of how your teeth feel in the morning after a long night of drinking...
Anyway, denture tabs work magic. And they are completely non-harmful.