I think of Schlumbergera x buckleyi / Schlumbergera truncata (aka "Christmas Cactus") as being more like tropical plants than succulents, but for some reason people call them succulents. They live in humid Brazilian forests and root at the base of trees in decaying material. One of my big discoveries for this plant was when I took a very sick specimen out of a generic potting soil that was high on minerals and low on organic material and placed it into a soil that was 80% bark. It thrived in bark, which somehow mimics the decaying soil in its native environment. My question: has anyone played around with adding a small fraction of peat moss to the soil mix for this plant, and did it have any effect good or bad?

In a very dry climate, that could be worth pursuing. I wouldn't use any peat for any plant, succulent or otherwise, where I am.

I mixed bark, perlite, and miracle gro cactus & palm potting mix for mine and it seems happy. I think the MG does have some peat in it.