They had me sign a very specific NDA where I could not state location, details of diet, heath, salary...not even disclose WHOM I WAS WORKING FOR.
That's not as outrageous as you seem to be making it, I can't imagine that anyone hiring a personal chef would want that person to go on and put on their resume: I worked for XYZ FAMOUS PERSON and had to handle DIET FOR PEOPLE WITH BAD GAS at their prestigious home at CELEBRITY ADDRESS HERE
"I worked for XYZ FAMOUS PERSON and had to handle DIET FOR PEOPLE WITH BAD GAS at their prestigious home at CELEBRITY ADDRESS HERE". It is not material for your resume and a massive no-no in terms of privacy, even without signing an NDA.
What you can put down though is something akin:
Personal chef to a family of four. My duties consisted of preparing XYZ meals every day, catering for specific dietary and health issues of the clients.
And whatever else is important for a chef on their CV, but that cannot even hint at who you've worked for, just do not go into any specifics. And if still in doubt, run it by a lawyer, it should not be expensive to get a comprehensive opinion. On a side note, that's something you should've done before signing any document you are not 100% sure about, but as we don't have a time machine, getting that now is the second best thing.