Migrate entirely to public `coverage` interface

[TheKevJames]

There are a few places in reporter.py where we reach into the internals of coverage to do what we need to do. It would be great if we could avoid doing this; wherever we can refactor to use the public interface, great. If the public interface needs to change, we can work with upstream to tackle that.

Once this is done, we'll be able to finally avoid getting broken by occasional non-major coverage updates.