Rework gulpfile

The gulpfile needs a major rework. Some existing problems include:
- Repetition of tasks (a `gulp all` runs the tests twice and the `styles` task 4 times!)
- The file change watchers are looking at the wrong directories and/or firing the wrong tasks
- There's a fair bit of spaghetti in there

In addition, there's also #1160, which proposes splitting it up into multiple files for readability and maintainability.