Improve type safety of internal classes

[delmyers]

There are a number of places where we cast from a base class to a derived class in our internal code, which could cause problems if a caller passes us an instance of an interface that we did not create internally. I suggest we:

1. Update our code to use virtual inheritance (instead of multiple inheritance). This will help us catch locations where we cast from a base class.

2. QI for the derived class. This will give us type safety.