There is no historical evidence to suggest that the Confederates showed any sort of sympathy for British rule over the United States. As you said, the Seal of the Confederacy actual depicts George Washington riding a horse.

I'm a Good Ol' Rebel is a folk song from lower class origins. The Declaration of Independence is essentially sacred to the United States, and declaring it hated was meant to insist that the South was a separate nation.

As for you second quote, throughout the war the Confederacy had delegations in Britain and France essentially begging for assistance. The French said they would support the fledgling nation if Britain would, but Britain said she would only offer the tacit support she was already providing; such as turning a blind eye to British shipbuilders constructing Confederate commerce raiders.

John Slidell led the Confederate delegation to France. James M. Mason led the Confederate delegation to Britain.

These men would have said anything if it meant the Royal Navy would smash the Union's blockade. Take it with a grain of salt.

(The South Will Rise Again)

Given that slavery was abolished throughout the British empire by 1843, any effort to return the Confederacy to British rule would also have resulted in abolition. Furthermore, the idea that the states rights obsessed Confederacy would have submitted to a foreign monarchy seems quite far fetched. For both of these reasons, the line about the declaration is likely representative of hatred for then Union rather than any desire to return to the British empire.

The American Revolution was celebrated by the white South in the antebellum era and the Civil War. I am not aware of any Confederates arguing it was a bad thing. In contrast, Confederates argued that they were the guardians of the Revolution and it was those damned Yankees who were betraying it. In Jefferson Davis First Inaugural he highlights the continuity between the new Confederacy and what the Framers of the United States Constitution intended: "We have changed the constituent parts, but not the system of our Government. The Constitution formed by our fathers is that of these Confederate States, in their exposition of it, and in the judicial construction it has received, we have a light which reveals its true meaning."

Fire-eaters and Confederates did not lionize all the founding fathers. In particular, Thomas Jefferson and the Declaration of Independence were problematic largely due to the rather inconvenient phrase "all men are created equal". Jefferson wasn't attacked just because abolitionists were misusing his words. There was a debate in the South over whether Jefferson was responsible for antislavery sentiment. The fire-eater William Yancey believed so because Jefferson "became imbued with the spirit of slavery emancipation; and under his powerful influence this mental poison spread through our political sphere..." Secessionists did like the parts of the Declaration that they felt they could use as precedent for disunion (conflating the natural right of revolution with the putative constitutional right of secession). By the 1850s, the ideal of Jeffersonian democracy came under attack from fire-eaters such as George Fitzhugh because of its individualism and celebration of the common (white) man.

There was no significant sentiment in favor of being governed by the UK in the Confederacy. If you check, footnote 71 for the paragraph you quote on page 134 of South Carolina Goes to War, 1860-1865 continues onto the next page and gives more support for the utter insignificance of monarchical sentiment in South Carolina .

Sources:

Cauthen, Charles Edward. South Carolina Goes to War, 1860-1865. Chapel Hill: University of North Carolina Press, 1950. https://books.google.com/books?id=fwuThAH_2jAC&pg=PA134

Crider, Johnathan B. (2009) De Bow’s Revolution: The Memory of the American Revolution in the Politics of the Sectional Crisis, 1850–1861, American Nineteenth Century History, 10:3, 317-332, DOI: 10.1080/14664650903122950

Davis, Jefferson. "Jefferson Davis' Inaugural Address." Civil War Trust. http://www.civilwar.org/education/history/primarysources/davisinaugural1.html

Fitzhugh, George. Sociology for the South Or, The Failure of a Free Society. Richmond, VA: A. Morris, 1854. https://archive.org/details/sociologyforsout00fitz

Peterson, Merrill D. The Jefferson Image in the American Mind. Charlottesville, VA: Thomas Jefferson Memorial Foundation, 1998.

Rubin, Anne Sarah. A Shattered Nation: The Rise and Fall of the Confederacy, 1861–1868. Chapel Hill: University of North Carolina Press, 2007.

Rubin, Anne Sarah. “Seventy-six and Sixty-one: Confederates Remember the American Revolution.” In Where these Memories Grow: History, Memory, and Southern Identity, ed. W. Fitzhugh Brundage, 85–106. Chapel Hill: University of North Carolina Press, 2000.

Walther, Eric H. William Lowndes Yancey and the Coming of the Civil War. Chapel Hill: University of North Carolina Press, 2006.