Continue to implement #2698:

- Add `core/base-service/index.js` (but hold off on moving the things it imports)
- Add shortcuts in `services/index.js` for Base*Service, errors, and deprecatedService. This file will be streamlined later to avoid cluttering it with rarely used bits.
- Apply consistent ordering of imports and use of `module.exports` in testers.
- Remove some renaming of imports.
- Remove obsolete tests here and there.