Thank you very much for taking the time to make a suggestion. I went through and changed the Output Format on everything from 8 bit to 16, and didn't seem to notice any changes, unfortunately. I wonder if it's related to how I'm generating the normals in the first place? I'm basically taking a black and white image, using an edge detection node to find the outline, and then running it through a series of curve, HQ blur and and invert grayscale nodes to generate the normals.

If there is a better way to approach this, I would love to hear any suggestions or thoughts. I'm almost embarrassed to say how long I've been working on this particular problem at this point.
After playing around a bit more, I was able to mitigate the issue somewhat by adjusting the curve nodes to sort of smooth out the output of the edge detection, and by adjusting the roughness of the material to have highlights that weren't quite as sharp. It didn't fix it completely, however.
Thank you again for your time!