Gaining a better understanding ultimately just took a lot of time playing with the equations and understanding how measurement and process noise/uncertainty get incorporated into the Kalman gain, and how that in turn affects the updated state estimate - e.g if you have zero noise in the measurement, you end up fully trusting your measurement. This tutorial [1] is the one I ended up studying. This is a case where memorizing the equations (with the help of Anki) helped me reflect on them and keep everything in my head long enough to improve my understanding.
