Rebuilding it will yield you better code over all since you know how to build it, but you need to ask yourself is this a wise choice. If it will just take you 2 hrs to do. I’d say go for it, and its TDD practice on something you know how to build.
If you do not think it will be a quick rebuild and do not want to throw away a decent amount of code, add some integration tests to cover major functionality and create that first test island, as you work and improve things add more and more tests to your app. This is good practice for working with legacy code bases, its hard to throw away code in a large or old code base. Rarely ever will business concerns and engineering concerns align enough to allow a rebuild from scratch.
You will probably need to use jasmine js or some other client-side testing framework to test the angular portion of your app. Using Rspec to do this is a pain in the butt and it comes with a lot of gotchas. I had quite a few issues just trying to get tests to run against angular even with browser engines like selenium or webkit. So I switched to using jasmine for angular apps.