Hopefully this isn't too much of a shopping question. I am looking for off-the-shelf silicon carbide P-N junction diodes, but all I can find are Schottky ones. Do P-N version ones even exist commercially?
SiC pn diodes are not commercially manufactured for one simple reason:
They have a forward voltage of about 3 to 4 volts.
For almost any purpose, either a silicon pn diode or a SiC schottky is a better choice. Despite the famous leakiness of schottky diodes, SiC ones (due to the properties of silicon carbide) tend to have leakage currents more in line with the leakage of a silicon pn diode than a silicon schottky.
If, for some reason, you truly need a SiC pn diode, it may be possible to use the the body diode of a SiC MOSFET where you've tied gate to source. The gate-drain junction of a SiC JFET might work as well, though these are not usually rated for much if any forward current.