RC does a great job with food allergies, but that's a tough one. I have no doubt they'll help you eat in confidence, but I'd definitely follow their advice and get a face to face meeting with the dining staff. They are really good about checking up on you each meal once they know your face.
If I had to pick a career all over again, it'd be in food allergy research. They've come a long way in developing readily available alternatives to (traditional) dairy allergies, gluten, egg, etc. But still plenty of people out there who struggle to enjoy a vacation away from home over food concerns.