Good summary of the uniformatarian/catastrophism situation Joe. I'd just like to add a few more things.
The doctrine of catastrophism strongly influenced geological ideas in the 17th and 18th centuries. Catastrophists believed features like mountains and canyons were created primarily in very rapid construction events, sometimes of world-wide scope. The causes were presumed to be unknowable and to be no longer active in modern times. This philosophy was an attempt to fit the geologic knowledge at the time with what was believed to be the age of the Earth. That number was based on Ussher's Biblical chronology. Both scientists of the time and theologians accepted this number as fact. But the work of Hutton and Lyell showed catastrophism did not explain the data.
One influenece you forgot to mention was John Playfair. Hutton wrote his book,
Theory of the Earth in 1788. But his writing style was extremely difficult to read. You can see an example of this style at
http://www.mala.bc.ca/~johnstoi/essays/Hutton.htm. Playfair presented Hutton's ideas in a much more clear and attractive form in his book,
Illustrations of the Huttonian Theory, in1802. However, it is true that the person most responsible for giving Hutton's idea light was Lyell, especially in his master work,
Principles of Geology, published in 11 editions between 1830 to 1872.
It must be emphasized again that unformitarianism only means that the geologic processes of the past were much the same as they are now. This is not an assumption, but an observation. Uniformism is not meant to be taken too literally. It does not mean the rates of geological processes were the same in the past as now, nor had they the same relative importance. There were periods for example when vulcanism was more important in shaping the Earth than it is now. Also, in the very earliest periods of Earth's existance, there were certain processes going on that do not occur at all today.