My coworker had the idea to drop bower from the chain, and simply use npm in its place. This change is very simple. In our package.json file he added entries inside the dependencies object for each bower package we had a dependency on, including its repository path.
"Class.js": "git://github.com/arinet/Class.js", <-- bower package
"angular": "=1.3.14", <-- npm package
"angular-cookie": "git://github.com/ivpusic/angular-cookie" <-- bower package
This simple change has allowed us to clean up our build tasks and make the process just a little simpler.