Even though this project started with the idea of using the VoCore module for the connectivity side, there are other ways that the rock could connect with WiFi

One potentially simpler method is to use an Electric Imp module. I've heard that these are relatively simple to get started with, and there's a bunch of tutorials to help you get started. Plus, the power management is much better, so while the Max power of the Imp is higher than the VoCore, the average or typical power shown on the datasheet is much less. 264mW instead of 1.3W. 

So I've bitten the bullet and gone and ordered one, along with an April breakout board. It may or may not arrive before the comp closes, but I may try it in the rock if the battery keeps going too flat with the VoCore.