No real help for you but I have Cooks and Rushes in my line, too. And I have a brick wall with my Cook's & Rushes. My Reuben Cook was born in 1739 in Hanover County, Virginia and he died in Elbert County, Georgia bef 1820. It is supposed that he might be the son of John who was born in Northampton County, North Carolina ( From my notes: 1756 Deed: John Cook of Northampton Co., NC, planter to Reuben Cook of N'hampton, 3 Jun 1756: Deed of Gift, Love & Affection to son Reuben.
250 Acres, p/o Grant to John Cooke of 1120 acres on June 1749. Adj acent Reuben, Henry Cook, & a Spring Branch.Wits: John Bailey, Henry Bagley, James Cook. (DB2/319-Northampton) 1759 Deed:
Reuben Cook & Mary, h/w of Sussex Co., VA to Lewis Johnson of same, 2 Jan 1759: 250 Acres, p/o 1120 acres granted to John Cook father of said Reuben 22 Jun 1749, & by the said John to the said Reuben 3 Jun 1756. (DB2/523-N'hampton) Per letter of Jake Cook, dated 24 Oct 1998, other N'hampton deeds name Henry, James, & John as other sons of John Cook(e). Jake Cook thinks that this is "Reuben Cooke, RS, who married Mary "Mollie" Daniel"." The names of the soms are similiar to those you give. I'm not sure of the timeframe of those you mention but families did use the same names in subsequent generations. I have no proof that Reuben ever was in SC but I know that Elbert Co., GA was just across the line. My Cook family moved on to Newton Co., GA and then a daughter married my ancestor, John R. Williams, and moved to Itawamba Co., MS. so their migration pattern was similiar.
Now for my Rush family, I have a Captain Mathias Rush born in either SC or Holland. He died in Greenville County, South Carolina in 1852. He was married four times and married to my direct line in Charleston, SC. He moved and lived in Spartanburg Co., SC being found in the 1800 through the 1830 census. By 1840 he was in Greenville Co. It is thought that he had a brother named Leonard...(no proof) and he lived in Fayette Co., AL and Tuscaloosa Co., AL. My Rush had a daughter who married a Burton in Spartanburg and moved to Fayette Co., AL. This Leonard who died in 2 April 1844 in Tuscaloosa Co., AL had a son named William Phillip. But his wife's maiden name was Phillip; so then it could only be coincidence and not a family name on his Rush side.
If you see a connection, I would appreciate your letting me know.