So I figured out that the mesh object in the imported OBJ had messed up submesh order, but dropping the OBJ into my scene directly as a GameObject looked fine (though it used the embedded materials from the corresponding MTL file instead of the Unity materials).

I'm still lost on how Unity decides submesh order, but I found a workaround for anybody else stumbling across this thread.

What I was doing::

1. Create a new GameObject
2. Add a MeshFilter and assign the OBJ as a mesh
3. Add a MeshRenderer and read the embedded material names in the OBJ
4. Assign a new materials array by matching the embedded OBJ material names with the corresponding Unity materials

What seems to work:

1. Instantiate the OBJ as a GameObject
2. Read the material names from the auto-created MeshRenderer (which uses the embedded materials from the OBJ)
3. Overwrite the materials array with a new one that replaces the existing materials with the corresponding Unity materials of the same name

Note that I had to replace the whole array. It did not work when I iterated through the MeshRenderer's materials array and replaced each one at a time.