Improve project organization

Proposed improvements to project organization.

This organization change has 3 goals:

1) Make the project more open and accessible
2) Make the project more scalable
3) Do this in an incremental way, without unnecessary refactoring

The actual organization change is covered in 6a99b8dea935be9228a47c84bcbfb7491e6e5584. Cosmetic changes are discussed in #9177 and #9178 
I'd add documentation here, natch.