Welcome, retroplaug. I also don't know what the Zebra Cactus is, but if it grows/looks like an aloe vera, you want to grow it in extremely well-draining soil. I use 1/3 potting mix, 1/3 course perlite, and 1/3 sand. I have grown aloe vera for decades and I don't bother to water any of mine until the leaves start to shrivel/pucker a bit. In the winter I only water mine only every other month and in the spring summer, perhaps every couple of weeks.
If this was my plant, I would remove it from the soil and let it dry out completely for a couple of weeks. Since I have fungicides, I would soak the plant in the fungicide mix for 3-5 minutes after removing it from its pot and then let it dry out for those two weeks. After the two week period, trim off any mushy/bone dry and brittle roots and/or leaves before re-potting. Be sparing with your watering for any succulent you grow.
Good luck.
