You're right -- after reading some of the peer responses, I realized that (I think...) my response is just how the Broadcast FM signal modulates the parts of the signal, and not how it actually 'locks on'. I'm still learning!
Another fun one, when you have IQ samples, is the polar discriminator: calculate x[t] * x*[t-1] where x* is the complex conjugate, and take the angle with arctan. Feels a bit like magic ("is that all?") but is justified by the theory.