As a human doctor, I'd suggest something different. This is because human doctors know if we tell a patient about a medication complication, especially if it's related to stomach issues, at least 50% of patients will automatically have the problems.That's why we often say, "If you have any problems with medication, call me", instead of telling you what complications are most common.
Can you get eggs from the Kahki Campbell ducks still? I'd have somebody else cook eggs and only the person delivering them know which ducks they came from. That way you can't be influenced by knowing. GI medicine is not my specialty. However, if you've cooked them, there should be no bacterial or parasite transmission. That only leaves allergic responses. Sometimes a person may not show an allergy for a bit, then once the immune system is primed, it can be a regular allergic response. But the human brain is truly a miracle. I can give you a sugar pill and if I warn you how a lot of people get sick and vomit when taking it, half or more, of the people will actually vomit! The more dramatic I am, the more people will get sick LOL
I suspect the actual proteins in the egg are the same. Therefore, you should not get sick from any duck eggs,if you had no problem with the first. The fact that you both react the same can also be placebo effect.