Simply from experience I can look at a unit name and provide a county reference for it. Let me know if you need to know about a particular unit.
After May 1862 a Confederate conscript could be assigned to a any company raised with his native state. Conscripts were taken to camp at either Talladega or Notasulga and then assigned to Alabama companies. Groups of conscripts reported to the Army of Tennessee or the Army of Northern Virginia. Some Alabama conscripts were assigned to regiments in the Mobile Bay defenses, while others formed conscript companies and performed provost guard duties.
As for your Hill family, I would be surprised to learn that another boy existed. The list of children on my previous post came from the 1850 and 1860 census, the 1860 list matching the one from 1850 quite well. As stories are repeated over time, names and relationships tend to change. "George" in your story might actually have been a cousin or brother-in-law with a different last name.
Concerning Henry H Hill's Confederate enlistment, you will recall that Federal forces occupied the Tennessee Valley from April through the end of August 1862. Little if any Confederate recruiting took place in that area while it was occupied. However, as quickly as the Tennessee Valley was recovered, about forty mounted companies formed almost overnight. In addition, several companies from DeKalb, Jackson and counties over the Georgia line formed the 3rd Confederate Cavalry.
Early rolls of the companies mentioned above should include Henry H Hill. Unless his name has been recorded differently (ex: Hall rather than Hill), I don't see him as a Confederate recruit. Perhaps someone else can improve on this.
If I may offer an opinion, prior to the occupation, most of the recruits mentioned must have been either neutral or Unionist. Many Confederates from the Tennessee Valley describe themselves as pre-war Unionist. Had it been otherwise, we would expect to find them among early war volunteers. Pastor Milus E Johnston places himself in this category, but writes that the behavior of Federal soldiers "rubbed a few drops of secession blood into our constitution."
The writer intended to take care of his family to the best of his ability. But lo and behold, he was not allowed to make a living by honest labor. On came the Federal army, laying waste to everything in their path, driving off hogs, cattle, horses and mules, arresting citizens and shooting innocent men who had never been connected with the Confederate army, and abusing women and burning houses. Before they seemed satisfied, they burned our family out three times, taking everything we had indoors and out.The Sword of "Bushwhacker" Johnston, pp 22-23.
Since Johnston did not leave his home north of the Tennessee Valley until late 1863, his remarks cover the first and second Federal occupation of the Tennessee Valley. However Johnston conveys a negative impression of Federal troops shared by many residents, regardless of political pursuasion. Following practices employed by European armies, German and other foreign-born soldiers are frequently mentioned among those who abused Southern citizens. The concept that the military should win "hearts and minds" of the people, if ever considered, took a back seat to a different idea: eliminating resistance by demonstrating the government's power to seize, punish and destroy.
If we knew more about political sentiment in your Hill family, they probably voted for the Democratic party like most other hill country farmers. De Kalb and other in north Alabama were known as "avalanche" counties because when the votes were counted, total always gave the Democratic candidate a large majority. I mention this because Abraham Lincoln described himself as an "old-line Henry Clay Whig." Whig candidates rarely won any office in De Kalb County.
People tend to act together according to family connections. It would be interesting to understand how and why some families supported the Federal occupation. Based on family research, sometimes they adopted positions counter to those of traditional family rivals. If a rival family took a particular position, your family (or mine) tended to find ways to oppose them. The war offered also offered a lawful opportunity to get even with with those who had wronged you in the past.