With two exactly identical birthdays for a Murley bride (13 Oct) and Hooper groom (14 Oct), it is hard to believe you are talking about a different Hooper/Murley family from the one I know.
But the Hooper/Murley family I know HAS to be different, because there is no way to reconcile the differences in data you listed with the documentation I have for the family I have studied.
The Hooper family I know moved from Cumberland Co., KY to Hardeman Co., TN. I will list some data for the Hooper/Murley family with which I am familiar:
A decade ago, Charlotte Holloway transcribed the burial info for Jeremiah Hooper and his two wives as follows:
Hooper, Jeremiah14 Oct1812-3 Oct 1891*
Hooper, Polly13 Oct 1828-15 Aug 1896
*I believe the 1812 birth date for Jeremiah is erroneous and should be 1818-he appeared as 31, 41, 52, and 62 on the 1850-1880 enumerations. Also, the local newspaper reported his death in an issue dated 31 Jul 1885, so I suspect his tombstone was placed at some point after his death, and when the birth and death dates became confused. A descendant with whom I have communicated gave me the birth date of 14 October 1818.
Existing Hardeman County, TN marriage licenses show
Jeremiah Hooper married first to Eleanor Gilmore on 12-30-1841 and next to Mary Murley on 20 Dec 1846.
Hooper: Jeremiah Hooper of Hardeman Co., TN is shown to be a grandson of Joseph Hooper (born 1770/75 per census data) in Joseph's 1842 will. Although Jeremiah was already married in 1850 and thus not living with a parent when the census occurred, he has been assumed to be a son of Joseph's son Richard Hooper, who had died between 1837 [when last appearing on a tax list] and 1840, when his widow Milly [Mildred] Hooper begins to appear on the census. Census data indicates this deceased Richard Hooper had been born 1802/4. Richard Hooper's heirs are mentioned in the 1842 Joseph Hooper will. The Widow Mildred Hooper is in the same age range as the oldest female in Richard Hooper's 1830 Hardeman Co., TN home. Her household in 1840 includes a male of correct age to be Jeremiah. She definitely was mother to Francis/Franklin M Hooper [b. 17 Sept 1832], for she is identified as such in F.M. Hooper's 1880 household in Hardeman County, Tennessee. However, I do not think I have definitive proof that she was the birth mother, rather than stepmother, of Jeremiah Hooper.
Murley: Mary Murley Hooper appears to have been a daughter of Daniel Murley. Daniel is listed in Hardeman County, TN in 1830 and 1840, and in Tishomingo County, MS in 1850 and 1860. His 1830 to 1860 entries suggest his birth in Kentucky about 1801/2. Nancy, the wife of Daniel Murley, was of similar age but born in NC, according to 1850 and 1860 entries. In 1880, Mary (Murley) Hooper indicated she was born in Tennessee and BOTH parents were born in Kentucky. Thus, I am not entirely confident about the identity of Mary (Murley) Hooper's mother.
On the 1820 census of Cumberland County, KY, a Daniel Murley is listed within a page of Joseph Hooper (grandfather to Jeremiah Hooper, the one who soon thereafter moved to Hardeman Co., TN). The 1820 Murley household in Kentucky shows husband and wife in the 26-45 range, but otherwise possibly could be identical with the Daniel Murley family that appears on the 1830 Hardeman County, TN. I am not 100% convinced the 1820 Ky Daniel Murley is identical with the 1830 TN Daniel Murley, but I do think it is at least probable that they were identical.
I have a marriage for Richard Hooper to Anne Forrest on 11 Feb 1786 in Hillsborough, Orange Co., NC, but neither Richard nor Anne Hooper are visible on any of the NC state enumerations (1784-86) nor on the federal census. Do you have any idea of their ages, or when they died?
I am confused about the location you gave. There is a TazEwell in Texas, but it is in Hopkins County. There isn't a Claiborne county at all in Texas.
Yet there is a Claiborne County in northeast Tennessee; that TN county has a community known as Tazwell. There are both Hooper and Hopper families (with interchangeable spelling in both families) around Tazwell, Claiborne Co., Tennessee.
Also, there is a Jeremiah Hopper (sic, two Ps, one O for surname on each occurence in the census) in 1840, 1850, 1860 in Claiborne County, TN - Jeremiah Hopper was born about 1821 in TN, and his wife's given name was Abigail. An existing Claiborne County marriage register lists the license for Jeremiah Hopper [sic] to Abigail Fulps on 22 May 1839, with the marriage solemnized on 24 May 1839. I had not been aware of any Murley connection in Claiborne County.