What other condition could produce the black leathery lesions that appear to be calciphylaxis?

Mixed ulcers. Some arterial ulcers can produce black eschar on their surfaces.
Pyoderma. Another equally difficult wound type caused pyoderma gangrenosum can present with a leathery surface as you suggest both have been considered untreatable in recent history and both get worse if debrided but calciphylaxis is related to calcium metabolism while pyoderma is autoimmune related to chroma disease lupus and other rheumatic diseases.
Calciphylaxis. Without pictures to describe exactly what you have, it is difficult to come up with a series of possible answers that would be meaningful. I am afraid that that i would need to direct you back to your primary care clinician or to your dermatologist.