Don't know if you're still checking this board, but if you are, you may be onto something with your Augusta Brewer. I've done a lot of Brewer research and didn't have them affiliated in any way with Murrell--in fact, hadn't even heard of Murrells.
Out of curiosity I checked the Hancock Co. Heritage books and found Murrells. Not a write-up, but there are Murrells marrying into and buried with, Brewer and allied families. Allied families for the Brewers in Hawkins/Hancock Cos TN include Cope, Odom, Beckler, Wolfe, Greene, Seals, Wilder and Trent, among others.
I did not find an Augusta Brewer, but there are a lot of unnamed descendants of Old Ambrose Brewer. Maybe some of the following information will give you a starting point for your Augusta.
1. Murrell Cemetery on Cool Branch Road. The earliest dates seem to be for John A. Murrell, b. 1820, d. 9/15/1865 and Martha Murrell, b. 1825 d. 10/23/1910. There are lots of other Murrells, plus a good showing of Greenes,and some Odoms, Wilders, Seals.
2. There is a William Greene, b. 1791 in Rowan Co. NC, d. 1873 in Hawkins Co. TN m. Ruth Slaton. Their children included: Nancy Greene m. Nicholas Wolfe Sterling Green m. Emoline Murrell Elizabeth Greene m. George W. Brewer Jeremiah Green m.1) Charlotte Murrell 2)Mary Wolfe John Greene m. Malissa Wolfe Ruth Green m. Nicholas Wolfe.
So your Augusta was certainly in the right place, at the right time, and hanging out with the right people to have been a Brewer. If she was in fact a Brewer, she's probably a descendant of Old Ambrose through one of his sons Known sons include Joab, Frederick, Howell Cobb, Prettyman, Ambrose Jr., Millenton and Pleasant.
William Greene's father, Jeremiah, came from Rowan Co. NC, while Ambrose Brewer came from Moore County. You might check Rowan Co. NC for Brewers. If your Augusta is from that area, she's probably from a different line than Ambrose
There was no write-up about the family, but it is mentioned in several places: