I have this information about the father Armstead BURCHETT and your James W BURCHETT. At least you can see Elizabeth [BUTLER] BURCHETT lived until the 1880 census and Elizabeth [LAWSON] BURCHETT did as well. I apologize for the incomplete nature of it but perhaps it will give you some direction.
Armstead Burchett, birth: 1795 @Charlotte Co VA; death: 1867 @Floyd Co KY; married: Elizabeth Butler (b: abt 1800 Sullivan Co TN) 14 Dec 1820 @Floyd Co KY;
1820 Floyd County KY Census: armsted burchett [armstead barthell]
1850 Floyd County KY Census: armistead 55 va/elizabeth 50 va
1860 Floyd County KY Census: armsted 60/elizabeth 60 tn
1870 Floyd County KY Census: elizabeth 70 tn; lucy 18 va; amstead 16 ky; surilda 13 F; dewey f 35; elz delaney 40.
James D Burchett, b.ca 1823 @Floyd Co KY; d: living 1860; married: Elizabeth Ann Lawson, b: abt 1830 Ky, liv 1880 Floyd;
1850 James D Burchett must have been in the 1850 census [perhaps with his parents] because I made the note he was "27yo and marked for could not read or write"
1860 Floyd County KY Census: james burchett 38 eliza ann30 matilda jane8; thomas6; martha ann4; mary2; james w.8/12 months; drury burchett23 laborer
1880 Floyd County KY Census: Liza A Birchett 51 Hsekepg. Widow KY Matilda J. 28 Dau. Single KY; Thomas25 Son" KY; Martha A.23 Dau" KY; MaryDau" KY; James20 Son" KY; Arta18 Dau. " KY; Louisa17 Dau" KY; Frank14 Son" KY; Josie11 Dau. " KY; Walter4 GransonTN; Elizabeth79 Gr.-Mother Widow.