I finally wired up the hall sensor and tested whether it was sensitive enough to detect magnetic flux changes as I move neodymium magnetics near it. 

The baseline was 2.5V as expected (analog serial signal 512) and I was able to get up to plus minus 25 on this serial value if two small magnets got really close. With more magnets (say a stack of around 10-15) the values were far more drastic (going into the 100s or 1000s depending on the polarity of the magnets).

This is the pinout diagram. The flat side down is the one where these correspond (although this can be checked by setting the serial monitor to the correct baud rate and making sure the baseline is around 512.

The Nano pinout is also here as a handy reference.

(We will be using GND, 5V, and 5 analog pins)