Dave, as long as your #define DELAY_START to reflect the pin state when the blink stops, the code should measure the duration to the next blink start.
The code above also hangs while timing but you should have enough time after the end of a pulse and the beginning of the next to update your servo. The problem with PulseIn for your app is that it only times up to three minutes.
You could use an interrupt to capture the transition but I am not sure its necessary. see here for more on interrupts with the arduino http://www.arduino.cc/en/Reference/AttachInterrupt