When Windows is left to decorate the title bar, it can look undesirable, and there is no way to readily change it in the way I wanted. So based on a few sources, I've come up with the following solution.
In my case, the issue was the title bar for emacs, but it is the case for many applications.
These steps will allow the continued use of accent color, but set the title bar to a color of your choice.
- Set the accent color in the Personalization > Colors interface to the color you want the title bar.
- Under "Show the accent color on the following surfaces", select "Title bars and window borders"