Can I increase the sensitivity of the Sparkfun electret breakout board?

You are welcome. Just open a book, and unbelievable, I find your sketch on p. 183, and it really doesn't have sqrt in code. Which is a mistake, RMS value is sqrt of the sum of square divided by number of samples. There only explanation not to do sqrt is get better performance (save time), and better sensitivity, sacrifice mathematical accuracy of results. But author is right about calculating running average, there is a division by averagedOver, which you skip in your code. You can improve performance of your code by replacing division (slow) with shifting operation:

runningAverage = ((( averagedOver - 1 ) * runningAverage ) + averageReading ) >> 4 ;