After a magical two week journey of researching Makefiles for the ESP8266 I've finally found what I consider to be the easiest and best solution. GitHub user thunderace has created an exceptional repository (https://github.com/thunderace/Esp8266-Arduino-Makefile/) that contains a great ESP8266 Makefile, a script that downloads all the libraries that are required for building, and an example project.

I created my own form of the repository (https://github.com/scintilla-aircheck/scintilla-arduino-ota/) where I included the library files directly so that I could clone/submodule/subtree this repo into any project that wants to build for ESP8266 without having to download the libraries with a separate command. I also plan on updating the example file to show OTA firmware update functionality.

To use my repo, just follow the instructions in the README.md to get a file structure like this:

scintilla-arduino-ota/
Makefile
your_project.ino
libraries/
   your_library/
      your_library_source.cpp
      your_library_source.h