There was no relationship between the two. Broadfoot includes only the names of officers from Blount's Battalion who signed a petition to the Secretary of War protesting General Bragg's orders. There are no original rolls of this organization, so the only records of Blount's Battalion are filed under the 58th Alabama Infantry Regiment. By the time the battalion was reconstituted in March 1863, it was understood that the 5th Battalion designation had been assigned to another Alabama command, so it was renumbered the 9th Alabama Infantry Battalion.
Robert P. Blount, formerly Captain of 1st Company “F”, 5th Alabama Infantry Regiment, was appointed Lieutenant Colonel May 13, 1862, to rank March 31, 1862, but addressed as such as early as January 19, 1862. Bragg's order relieved him of command on April 28, 1862. He later was placed in charge of the provost guard of Longstreet’s Corps, Army of Northern Virginia.
John W. Inzer of St. Clair County, youngest delegate elected to the Alabama Secession Convention, provided a history of Blount's Battalion, its dissolution and reformation. I know of few other Confederate commands which were dissolved and later recreated. In fact, only the 12th Alabama Cavalry Battalion comes to mind. Here's a link to a site where part of Inzer's prison diary may be read:
http://www.archaeology.org/cgi-bin/site.pl?page=online/features/civil/index
Judge Inzer unfurled the flag of the 58th Alabama at a reunion in Odenville AL in 1911:
http://members.aol.com/stclairal/Reunion.html
A Florida company ("Howell Guards") and a company from Virginia were briefly attached to Van de Graaf's 5th Alabama Battalion, not Blount's.
Here's a list of the original companies of Blount's Battalion and their captains:
Company “A” of Saint Clair County “Springville Volunteers”
Sheriff Brewster. Commission vacated April 28, 1862. Later served as 2nd Lieutenant of Company “K”, 18th Alabama Infantry Regiment.
On December 27, 1861, members enlisted for twelve months service at Ashville, Alabama.
Company “B” of Fayette County
R. Allen Smith. Commission vacated April 28, 1862.
Members mustered for twelve months in Confederate service on December 27, 1861.
Company “C” of Jefferson and Saint Clair Counties
John M. Franklin. Commission vacated April 28, 1862. Later served as a member of Company “E”, Barbiere’s Alabama Cavalry Battalion.
This company was accepted for twelve months in Confederate service on December 27, 1861.
Company “D” of Saint Clair County
J. M. Thomason. Commission vacated April 28, 1862.
On January 20, 1862, officers and men enrolled in Confederate service for twelve months at Ashville, Alabama.
Company “E” of Butler County “Ben Edwards Grays”
Randolph Owen. Commission vacated April 28, 1862. Later served as Captain of 2nd Company “H”, 1st Confederate Infantry Regiment.
On January 27, 1862, at Greenville, Alabama, members mustered for twelve months in Confederate service.
Company “F” of Calhoun County
Samuel Durham McClelen. Commission vacated April 28, 1862; appointed Captain of Company “B”, 18th Alabama Infantry Regiment. Later served as Captain of Company “F”, 58th Alabama Infantry Regiment. [DAB4:1092]
Mustering as Company “F”, Blount’s 5th Alabama Infantry Battalion, this command enlisted for twelve months in Confederate service on February 11, 1862.
Company “G” of Saint Clair County “Saint Clair Greys”
Levi Lloyd. Commission vacated April 28, 1862. Later served as Captain of Company “K”, 18th Alabama Infantry Regiment.
Members enlisted for twelve months in Confederate service on March 1, 1862, at Ashville, Alabama. After April 28, 1862, they merged with Company “A” to form Company “L” of the 18th Alabama Infantry Regiment.
Company “H” of Dallas County
Elias W. Fort. Commission vacated April 28, 1862. Later served as a member of Company “E”, Lewis’s Alabama Cavalry Battalion.
Officers and men enlisted for three years or the war, February 28, 1862. Reporting at Montgomery, Alabama, March 20, 1862, they became Company “H” of Blount’s 5th Alabama Infantry Battalion.
Substantial discussions about this unit exist in the message boards archives.