Your approach to locating the intolerance is correct.
I would first start with testing 5 foods that are most important for me.
Beware, sometimes, you will be able to tolerate 5 different foods if you take each one of them separate... but if you combine all 5 in the same meal, you may have problem digesting it, and as a result it may trigger cheilitis.
Another thing: sometimes people are able to tolerate raw food, but not if the same food is cooked. That is often case with tomatoes, peppers, and other different vegetables.
For some other food it may be opposite, cooked may be OK, but not raw.
By far, the most common problem with pinpointing triggers and intolerance is a fact that many people may tolerate many foods as isolated, but not when combined with many other foods, or when added spices.
Also, the amount of food eaten is a huge factor in food intolerance.
The smaller amount consumed, the more different foods you can tolerate.
Please check Blood Type Diet
lists, 80% of people or more often have tolerance problems with the "Avoid" foods.
Any test (intolerance or allergy) you take can help pinpoint triggers.
Keep us updated.
Sometimes, trigger is only a trigger while you consume a food that you are allergic to.
Like people allergic to wheat, may have many other triggers while eating wheat. Once they stop eating wheat for 30 days, other trigger foods top being triggers ...