Now into the George Mills line (this was another theory, eliminated Fall 1999, data preserved to help others):

Another family member gathered the following information which certainly looks to point in the right direction but nothing is authenticated:

"The only record of the Revolutionary War on Thomas (m. Eliza Gaskill) b. 29 Sept 1763, d. 26 Feb 1864 is a photo of his old headstone which reads Thomas Mills, PVT, Co. 3, 2 S.C. REGT, REV. WAR, SEP. 29, 1763, FEB. 26,1864; Sandrun Churchyard, Hebron, KY. The headstone shown in an article from the "The Kentucky Post" (Saturday, October 20,1990) shows also the inscription above plus "War of 1812" on it. The heading for the article is "Kentucky pioneers laid to rest in style." The article says that on the back is inscribed "Swamp Fox Soldier" and "Ky. Corn Stalk Militia." The article goes on to state "Thomas Mills was born Sept. 29, 1763, in Long Island, N.Y. He moved to South Carolina with his father and older brother and signed up with Lt. Col. Francis Marion during the Revolutionary War. Mills was only 12 or 13 years old at the time. He served with the 2nd South Carolina Regiment and Marion's group, the Swamp Fox Soldiers, from 1776 to 1779." It also says he later traveled to KY and OH where he was a scout and Indian fighter and that was where he met Daniel Boone and Simon Kenton. And "In 1786, Mills was among several families who petitioned the Commonwealth of Virginia to establish the towns of Washington and Limestone, later known as Maysville." Says further that Mills married Lydia Wilson in 1786 had several children then she died after son Edward was born in 1805. The following year he married Lydia Cachel (note: 12 March 1806). They moved from Clermont Co. to Cjevoit and Mill Creek in Hamilton Co. He had 13 children by both Lydia's. Served in the Corn Stalk Militia between 1791 and 1799 and fought in the War of 1812. Said the family left Mill Creek in 1835 and eventually settled in Bullitsville, Boone Co., KY "

This is interesting as it suggests a link between the Mills family and what we know from the Kirwin Family Ballad which mentions that Martha and Patrick's son Frank was named for the Swamp Fox. 

Charted it looks like this:

I have since learned that the Thomas who married Eliza Gaskill is a younger relative of this Thomas and the marriage was much later as well. Further research into this line has produced this line down to Hope III's family group. I am trying to fill out all the members of the families of Hope III's sons looking for a Martha b. 1835-38 (!) - there are LOTS of Martha's in this line (while there are conflicting views; much of the vital information listed below can be supported by information found in "A documentary history of the family of Mills," by Lewis D. Cook, Philadelphia, 1939):

[1] George Mills b 1595/1600 (England, perhaps Yorkshire?) d 17 Oct. 1694, (Hempstead) Jamaica, Queens Co., Long Island, NY m Rebecca Tanner Abt. 1629, USA?
[1.1] Samuel Mills b 1631, Jamaica, Queens Co., Long Island, NY  d. Friday, March 18, 1726/27, Jamaica, Queens Co., Long Island, NY; m Susannah Palmer Abt. 1658 (names listed below are from his will; 16 children known but not all named - the list below is tentative and the exact birth order may be incorrect - if you can help sort this out, please contact me):
[1.1.?] Samuel Mills, Jr. b. 1659 Jamaica, Queens Co., Long Island, NY, d. 1719, Greenwich, CT; m. 1693 Sarah Denton (occupation Blacksmith)
[1.1.?.1] Samuel Mills, III
[1.1.?.2] Clement Mills
[1.1.?.3] Susannah Mills
[1.1.?] John Mills b. 1661, d. 15 April 1706, Stamford, CT; m. 1) ? Mary ?  2) 1681 Susannah
[1.1.?] James Mills b. 1663, d. after 1691 likely New York City
[1.1.?] Hannah Elizabeth Mills, b. 1665, m. bef. 22 Jan 1682/3, John Smith
[1.1.?] Andrew Mills b. 1667, d. April 1702, Bedford, NY
[1.1.?] Susannah Mills b. 1669
[1.1.?] Rebecca Mills b. 1671
[1.1.?] George Mills b. 1673
[1.1.?] Clemence Mills b. 1675, d. 1709; m. 1697, Bedford, NY Nathan Clark
[1.1.?] Mary Mills b. 1677
[1.1.?] Martha Mills b 1679 d 1719 Long Island, NY, m 1702 Samuel Denton (no issue)
[1.1.?] Hope Mills, Sr., b 1681 Jamaica, Queens Co., Long Island, NY d 1737 m Martha ?, 1707 (Hope Mills Jr. died early in life, Hope Mills Sr.'s Will names children, leaves $ to grandson Hope III, "only son of my son Hope Mills deceased")
[1.1.?.1] Amos Mills b 1709 d 1774 m Ruth ? 1738 - all Jamaica, Queens Co., Long Island, NY; 7 children
[1.1.?.1.1] Martha b Aft. 1738 m ? Ludlam
[1.1.?.2] Hope Mills, Jr., b. 1711 Jamaica, Queens Co., Long Island, NY, d. by 1737,  m abt. 1732 Margtie Strigham
[1.1.?.2.1] Margtie b 1733 Jamaica, Queens Co., Long Island, NY
[1.1.? 2.2] Hope Mills III b 1735/7, Jamaica, Queens Co., Long Island, NY, d. after1811, Columbia Twsp. Hamilton Co., OH; m 1756/58 Jamaica, Queens Co., Long Island, NY wife unknown (family left Long Island for SC - possibly near Columbia; in 1775, he and sons Thomas and Amos served with Lt. Col. Francis Marion's "Swamp Fox" Soldiers, 2nd SC Regiment, 3rd Company; was alive 1810-13 in Ohio, the name "Hope" also shows up in Vicksburg, Civil War, but it unclear which generation the named "Hope" represents); the 1st four children of Hope Mills III are known, the 2nd four children are possible but unproved - please contact me if you have information on these children):
[1.1.? 2.2.1] Edward Mills b. after 1756, m. Mary Martin
[1.1.? 2.2.2] Amos Mills b. abt. 1760 m Catherine Gulick (said to have served in 1775 with Lt. Col. Francis Marion, but I have not found proof; I have been told Amos went to Hamilton Co., OH after the Revolution and freed his slaves there, no proof yet; and that Amos and brother Peter married sisters in Delphi Township, Hamilton Co., OH; I have found an Amos Mills back in Jamaica, NY in 1790 Census - 3 males over 16, 1 male under 16 and 4 females, but do not know if this is the same Amos; no Amos shows up in the OH Census in 1820, but Hope, Thomas, Peter and Edward do show up)
[1.1.? 2.2.3] Peter Mills, b. abt. 1770 m Hannah Gulick (Will of Tunis Gulick, father of Catherine and Hannah mentions Amos and Peter Mills)
[1.1.?.2.2.3.1] Hannah Mills b 10 July 1794, NY d 18 July 1868, Mill Creek Township, Hamilton co., OH, m Lyman Crary 15 April 1816, Springfield Township, Hamilton Co., OH
[1.1.?.2.2.3.2] Samuel Mills b. Abt. 1797, NY
[1.1.?.2.2.3.3] Maria Mills 13 November 1799, Cincinnati, OH, d 25 July 1882, Greene Township, Hamilton Co., OH, m Epheriam D. Williams 25 December 1818, Hamilton co., OH
[1.1.?.2.2.3.4] Peter Mills Jr.
[1.1.?.2.2.4] Thomas Mills b 29 Sept 1760, Jamaica, Queens Co., Long Island, NY d 26 February 1864, Bullittsville, Boone Co., KY m Lydia Cachel (Cashell,Cashwell) 12 March 1806, Lebanon, Warren Co., Ohio (I did find Thomas' name on the list of soldiers known to have served with Francis Marion, but not Hope II or Amos; 1780-81, age 17, Thomas was captured and held by Indians in TN for one year; he escaped into the KY and OH wilderness and met Daniel Boone, Simon Kenton, Andrew Jackson, John Cleves Symmes, Gen. Harrison, Ludlow and other scouts - became a scout, 1783-85; 1786 Thomas Mills signed Petition to Commonwealth of Virginia to establish Limestone [now Maysville] and Washington, KY

• Here is the information I have been able to gather so far on the descendants of Thomas and Lydia Cachel Mills. The data seems to prove our Martha is NOT of Thomas' line; so now I am pursuing the descendants of Amos and the other sons of Hope III:

[1.1.?.2.2.4.1] Ruth b Abt. 1807, possibly Warren Co., OH, m Murray Warren
[1.1.?.2.2.4.2] Hope (IV) b March 1808, OH, m. 1) Rebecca Martha Armstrong, 31 March 1844, Cincinnati, OH (d. 1847), 2) Jane Willa Bartles, 9 January 1849, Lewistown, Fulton Co., IL (Hope and Jane do show a Martha, but their marriage date makes it too late to be our Martha)
[1.1.?.2.2.4.3] Catherine b 18 November 1810, Goshen Township, Clermont Co., OH, d 24 January 1862, m James C. Boyd Abt. 1838, Cincinnati, OH
[1.1.?.2.2.4.4] Peter Mills b 4 March 1811, Mill Creek, Hamilton Co., OH, d 14 May 1896, Glasford, Fulton Co., IL m Lucinda Dougherty 14 February 1836, Greene Township, Hamilton Co., OH - they show a daughter Martha J., but she is not born until 5 January 1845 when our Martha would have been 10 - family shows up 1820 & 1830 in Ward 2, Cincinnati, Hamilton Co., OH, 1840 in Whiteside Township, Hamilton Co., OH and 1850 in Burlington township, Boone Co. KY)
[1.1.?.2.2.4.5] Martha Mills b 16 October 1813 Mill Creek, Hamilton Co., OH d 9 August 1876, Farmington, Fulton Co., OH, m Robert Greenwell 10 March 1836 (Thomas Mills shows up in the 1850 Burlington Township, Boone Co., KY Census living with family of Robert and Martha Mills Greenwell; Lydia has died in 1850 before the census is taken. 1853-54, they go to Illinois)
[1.1.?.2.2.4.6] Thomas Mills b 13 March 1817, Mill Creek, Hamilton Co., OH, d 5 July 1888, Hamilton Co., IN, m Rachel Warren 12 August 1839 (NOTE: this may be an error! Thomas who m. Rachel Warren may be the son of Alexander Mills, not Thomas and Lydia - and the children of this couple were not born until after 1840)
[1.1.?.2.2.4.7] Lydia Ann Mills b 1821 Mill Creek, Hamilton Co., OH, d 1850, m Ezrom H. Scothorn Abt. 1844
[1.1.?.2.2.4.8] Matilda Jane Mills b 16 January 1827, Mill Creek, Hamilton Co., OH, d 3 May 1913, Hebron, Boone Co., KY m Christopher Barlow 16 January 1845, Bullitsville, Boone Co., KY
[1.1.?.2.2.5] ? William Mills ?
[1.1.?.2.2.6] ? John Mills ?
[1.1.?.2.2.7] ? Jacob Mills ?
[1.1.?.2.2.8] ? Elijah Mills ?
[1.1.?.3] Nathaniel Mills b. 1713 Jamaica, Queens Co., Long Island, NY, d. 1779
[1.1.?.4] Obadiah Mills b. Jamaica, Queens Co., Long Island, NY, d. 1777
[1.1.?.5] Deborah Mills b. Jamaica, Queens Co., Long Island, NY
[1.1.?.6] Martha Mills b. Jamaica, Queens Co., Long Island, NY
[1.1.?.7] Catherine Mills b. Jamaica, Queens Co., Long Island, NY
[1.1.?.8] Stephen Mills b. by 1737 Jamaica, Queens Co., Long Island, NY, d. 1753
[1.1.?] Aurelius Mills b. 1683, d. 18 April 1759, Flushing, NY; spouse unknown, 1 daughter, Elizabeth
[1.1.?] Alexander Mills b. 1685, d. October 1732; m. 1709, NYC spouse unknown; 5 children
[1.1.?] Ephraim Mills b. 1687, d. 1768/9; m. 1711 Charlotte Pct., Dutchess Co., NY Susannah; 8 children
[1.1.?] Zebulon Mills b. 1689, d. 1773; m. Ann Wright
[1.2] Zachariah Mills b. abt. 1630-44; d. 1696, Jamaica, Queens Co., Long Island, NY; m. 1675 Abigail Messenger Darling
[1.2.1] Zachariah Mills, Jr.
[1.2.2] Abby Mills
[1.2.3] Sarah Mills
[1.3] Jonathan Mills b. abt. 1640-45; d. 1714-17, Jamaica, Queens Co., Long Island, NY
[1.4] Bethia Mills