What a puzzle.
I'm with Lisa, and others who suggested giving her nothing but her kibble for a month, and seeing what her response is to that. The strategy here is by process of elimination, or addition, you can possibly determine what is causing, and/or helping, this issue. It won't be a short experiment, but it will hopefully help isolate the problem(s)
If she reacts to just the kibble, try changing it. Change to grainless. Change the brand and protein source. Change the number of times a day you feed, or the time of day. I wouldn't add anything additional to the diet, no supplements, no meds, nothing else until you've determined as definitively as possible that her kibble is, or isn't, the issue or part of the issue.