And of course no matter how many animals we study today, none of them are in a state of change with some parts becoming others or nascent organs developing.....
More than anything, I think this speaks to the difficulties in conceptualizing the process of evolution. There is this idea that life is only evolving if there is a half-way version of things; like a half a species or half an organ or something.
Yet everything is always going to be fully formed because there is no such thing as a half-formed animal or organ. Rather, there are different biological forms that serve various functions and specializations, including multiple functions.
This is where I think it helps to look at existing extant species in different environmental niches to see how different physical structures can vary across different organisms.
A great example is found in various mammals ranging from fully terrestrial to fully acquatic and everything in between.
For example, consider the mammal feet/paws of something terrestrial like this rabbit:
Then compare to a semi-aquatic mammal like a beaver or otter. Beavers and otters have webbed feet, providing for greater utility in the water:
Then look at seal flippers which still retain some of their inherent digits, but are more "flipper" like for greater utility in the water:
Finally you have whales and dolphins which are fully aquatic and no longer possess individual digits on their flippers (although the underlying skeletal still has them):
When you look at these variations in the animal kingdom it becomes a lot easier to conceptualize how things can evolve over time and yet still be fully formed organs or structures.
(edited: Pictures aren't showing up for some reason. You can google images of what I was listing though; there are plenty to be found.)