I wanted to update quickly to say the rash is almost completely gone!!!
We saw major improvement as soon as we cut things from her diet. We also used the yeast medication - I don't think that was it, though. As soon as we cut out eggs, oats & raw apples, the stools improved overnight (no more mucous), she went back to 1-2 stools a day (instead of 6+) and the rash improved dramatically, with or without diaper cream.
So this tells me it was most likely a food intolerance. I remembered two other foods I had introduced around the same time, dates & honey. Dates were the only dried fruit we had in the house for awhile, so I cut up maybe one each day to give her as I fixed something more substantial, and honey is our main sweetener around here, so I started letting her have bread with honey on it.
We have continued giving her bread and she seems to have no adverse reaction so I doubt it's gluten. Whew! No one else in our family is GF, but we have many diet restrictions as it is (chemicals & salicylates / Feingold diet basically) so cutting gluten too was something I dreaded.
I believe I also gave her a few bites of my cereal during that time that had raw milk on the spoon, so I cut all milk exposure too, and cut mine back again.
So she's off oats, eggs, milk, dates, raw apples & honey. I am eating all of the above, with the milk in strict moderation with no ill effects in her diaper. She has also eaten a piece of a baked good with an egg added to the batter with no ill effects (dh didn't know). So I don't know if eggs are my top contender. I think once the rash is all the way gone with no traces whatsoever I'll reintroduce from the back of the list up, with eggs and oats being last.
Thanks everyone SO MUCH!! Your input here was enormously helpful!