I must have just missed your response years ago, because I was notified of these answers today.
Another piece of information I found today was that Henry and Elizabeth's sister Rosa was also known as Rosanna. This is from a print-out of a Descendants' file (I have no idea where I got this) titled Descendants of Valentine Eckel. The reason I think this piece of information is important is that I have a copy from a book called Tennessee Land Grants and it shows Henry et al, Amos, and Rosannah as grantees in Jackson County, although Amos and Rosannah are also the names of two of Henry's children.
EAKLE, Amos (J) 1825, 300a, M dist, bk 3 p 312, g#2003
EAKLE, Henry et al (J) 1825, 300a, M dist, bk 3 p 312, g#2003
EAKLE, Rosannah (J) 1818, 10a, G dist, bkP, p281, g#12731
Henry's Rosannah would have only been eight years old in 1818, but Amos would have been 21 in 1825. Also, Henry and Amos' grants are in the same book, and have the same page number and grant number, but Rosannah's is totally different.
I also have a copy of a land transaction that is very hard to read, but I will try to transcribe it. I will put in ?-marks where I cannot decipher letters. I got it from microfilm at the TN State Library:
A10094: Survey Pat 78th
Rosanna Eakle ??? originally of Rich W Smith by virtue of certificate A887 ???? by the ????????? of West Tennessee Entry for acres of Land in Jackson County on the waters of line creek of Barrier River Beginning at a ?????? Dogwood ???? southwest corner to Martins Survey onto Rosanna's Eakles East boundary line of the land wherein she now lives running East to Samuel Hodges survey then south ???? ?????. 14th March 1816. John Murry, ????
Since this was in 1816 and Henry's daughter would have only been 6 years old, it makes me think a third sibling moved to Jackson County: Rosa. It is pretty rare to see old records in a woman's name. I know from things I have seen online that Rosa married John P Mitchell of Augusta County VA, but I wonder if that happened later in life. She would have been 30 in 1816.
I know my gggg grandmother, Elizabeth Eagle, came to Jackson County with her husband, John Clements, in 1806 according to his Application for a Revolutionary War Pension.
In the same book (TN Land Grants) it shows John Clements with two grants, one in G dist like Rosanna's:
CLEMMONS, John (J) 1811, 60a MTN dist, bk 4, p 743 g#2968
CLEMMONS, John (J) 1812, 60a G dist, bk P, p 309 g#2968
Do you have any more information about Rosa Eakles or her husband John P Mitchell?