Invoke getClassLoader() from doPrivileged.

When we're retrieving class loaders for internal use (not passing them
to the outside world) we need to ensure that they're retrieved using
a doPrivileged block.
Streamline retrieval of method handles.

- Use Lookup.PUBLIC whenever looking up handles to public methods.
- More consistent use of Lookup.findOwn* methods with less repetition.
Remove unused method.