There is no problem with using the negative form of a verb + n janai to form a tag question — in fact it is very, very common and いけないんじゃない is a good example.
I would only say that even though 食べたくないんじゃない is perfectly grammatical, it is not quite a real world example. A tag question is a euphemism for what you suppose to be true.
If 食べたくない is about yourself, んじゃない suggests you are not sure about your own state of mind. (To soften 食べたくない you can use かも(しれない), (んだ)けど, etc.)
If 食べたくない is about somebody else, you presume to have an idea about a third person's mental state — which contradicts the "curious unwritten rule which states, in essence, that you cannot presume to know the intimate details of a third person's mental state".
I think this might be the reason ～たくないんじゃない has only three hits in the Balanced Corpus of Contemporary Written Japanese (of 1238 results for ～ないんじゃない and 6790 results for ～たくない).