I believe I figured out why I was receiving the error.

So, moving forward I believe these are the steps I should follow to ensure my formatting is not affected by another's Normal.dotx.

Create a new template. I add it to my document through the Template and Add-ins dialog box with Automatically update document styles checked. Then, I can find and apply my new styles. When done formatting, I uncheck the Automatically update document styles and I'm good to go.

Have I finally grasped this? (I truly appreciate your patience.)