I realized my initial post probably did not have enough information. Let's try that again:
The core of my issue is that I am having trouble applying a triplanar map to a normal in the bump channel of a corona material.
I get similar and predictable results when I place the texture inside a triplanar map in either the diffuse or reflectance channels. I can switch the texture tag projection to any type, and the mapping does not change. This is as expected, from what I understand about the triplanar map.
Diffuse Only (Regardless of Projection):

Reflection Only (Regardless of Projection):

The real weirdness starts with the normal map. As mentioned in my original post, to simulate car paint flakes I have a tiles shader with tiles colored a solid R, G, and B to give random normal directions. At a small enough scale, this would look like shiny flecks. However, when I do my same triplanar tests with the normal slot, the
outlines of the normals don't change, but the
angles of the normal do. And it's consistent for certain groups of projections, too, which is bizarre.
Examples (All same shader setup, but switching projection types):
Cylindrical/Spherical/ShrinkWrap:

Flat/UVWMapping:

Cubic:

Frontal:

Spatial (Almost-but-not-quite the same as Frontal):

Is there an ideal projection type in this situation? Is it supposed to shift this way? Any insights?
Here's my shader setup, it's not terribly complex:

Thanks!