I think we use the word random too often. At the fundamental level (where it really matters) the chemistry is not random. Chemical bonds and long chain polymers follow a very distinct set of "rules". But remember, biochem is not my formal educational background. So if I have posted in error, I hope I will be corrected.
Nor is the deeper physics underlying the chemistry.
My own big issue on these threads is the carelessness with which the term "random" is tossed around.
To Sabertooth's point about reshuffling genes, humans contain genes for gills and probably some other stuff (wings would be cool, but I don't think we could fly). Look at human embryonic developmental characteristics. But genes are added and destroyed. There are simple viral vectors for some activity and bacteria can swap DNA readily. There are also situations where DNA can become truncated. Again the processes are not well understood.
Technology has reached the point where these mechanisms can be described over the next several hundred years or less. There's a lot of data, but the procedures are becoming automated and computer power and memory are no longer a constraint. This is a key point in history where this technology can benefit us in the hands of a free people or create God knows what suffering in the hands of people like x42. As a Christian, I'm saying we're better off having this technology in the hands of people who have moral values and who value life.