I have now had it confirmed that I have a dairy intolerance as opposed to a true dairy allergy. After having hives for a week (from an unrelated cause), I finally saw an allergist who did some skin-prick tests on me. While some of the food test areas did appear red, none of them developed a weal of 3mm or more. It was pointed out to me that I have very sensitive skin because the control test of saline also turned red (which it shouldn't have).
He did say that, since it isn't a true allergy, it wouldn't kill me to cheat and have dairy once in awhile. I will keep that in mind, but for now I'm still staying away from it.
While I was there I tried to ask the doctor about the meaning of just a positive IgA test when the rest of the celiac panel was negative. He wasn't familiar with the test I was asking about. All he could tell me was that there is no test for NCGS. So I'm still stumped on that one.