I don't see what you mean when you see that creationists define information deliberately so that it cannot be increased through random mutations. The definition of information that they use, at least from what I have read, is the same definition given by information science.
Actually, it isn't. They make up their own definitions, such as Complex Specified Information.
The changing of a bird's beak or wing-shape, to make it more apt at doing one thing may be beneficial, but it does not require any new information, and thus cannot be used as an example of evolution.
This is exactly what I am talking about. If this is not an example of new information then evolution does not need to produce new information in order to produce the biodiversity we see today.
The new information needed by evolution can only come by incremental steps, and there is no example whatsoever of any new information being added to DNA that benefits it.
That is exactly what you described with the bird's beak and wing, and yet you say that is not new information.
Even if you say that evolution does not require an increase in complexity, but can also be characterized by a decrease, that still doesn't explain how the increase occurs by means of that same evolution.
It occurs through mutation and selection. Whether or not creationists want to call this "new information" has little to do with the reality that evolution does occur.