Thanks everyone.
The nutrient hypothesis is a bit hard to digest as I have another of these plants (schlumbergera) that has been watered and fertilized similarly and has not had these problems. The affected plant gets more sunlight, but I don't think that is related. The light is indirect, and the plant was placed in its current location after the problem started. Additionally, if it was tied to nutrients, then I am not sure why half the plant has been largely symptom free. I would think root or stem damage or pests would be more likely to cause localized damage that spreads over time. Regardless, I can certainly try to fertilize with a 3-1-2 (or other recommended) mix.
In general, I water the plant using well water. Our water is a bit heavy on TDS. However, again, I don't think this is the problem. The same water is used for the other unaffected plant as well as most of my other plants. Every 2 years I'll repot due to deposits in the soil. However, I had the affected plant repotted after the problems emerged, so I don't think dissolved solids aggregating in the soil are to blame.
I have a product, Monterey Complete Disease Control, that I've used to successfully treat other plants suffering from root rot due to overwatering. Again, I have no reason to believe overwatering is the culprit here, but treating with the Monterey product might be one option.