With the introduction of new `AdminSite` and `ModelAdmin` classes for
our new administration UI, it's important that we set a precedent of
using these new classes for all model registration, even though the new
versions are compatible with the old ones.

This change switches all model registration to use our new `AdminSite`
explicitly, and switches all `ModelAdmin` subclasses to use our new base
class.

Testing Done:
Unit tests pass.

Verified that these were registered correctly in the admin UI.

Reviewed at https://reviews.reviewboard.org/r/11039/