I think it's important to understand this whole "how many owned slaves" question realistically.
The usual answer is "very few owned a lot of slaves", overall in 1860 only 5% of eight million Southern whites owned slaves, and of those only a few thousands owned 100 slaves or more.
But if you ask, "how many whites lived in slave-holding families?" -- then the answer is quite different, and needs to be understood from the perspective of Deep South compared to Upper South and Border States.
Seven states of the Deep South (South Carolina to Texas) included 2.5 million whites with 2.3 million slaves.
Whites lived in 677,000 families of which 181,000 owned slaves = 27% of white families owned an average of 13 slaves in the Deep South.
Four Upper South states (Virginia to Arkansas) included 2.9 million whites with 1.2 million slaves.
Whites lived in 668,000 families of whom 133,000 owned slaves = 20% of white families owned an average of 9 slaves in the Upper South.
Four Border States (Delaware to Missouri) included 2.7 million whites with 427,000 slaves.
Whites lived in 565,000 families of whom 77,335 owned slaves = 14% of white families owned an average of 6 slaves in the Border States.
So, overall the 1860 average is 21% of 1.9 million Southern white families owned on average 10 slaves each.
Yes, these numbers are somewhat different than I've posted before and represent corrections.
The biggest surprise is to learn that Deep South (27%) and Upper South (20%) had somewhat fewer slave-holder families than I'd calculated before.
Border States at 14% overall are slightly higher, ranging from 3% in Delaware to 11% in Maryand & Missouri to 19% in Kentucky.
The numbers help tell the story of why the Confederacy was more successful persuading Deep and Upper South states to join it, than it was in Border States.
The data cited there looks a lot like some of the other sources I happened on and some of them noted in their analysis that the data from the 1860 Census they examined was incomplete in one way or another due to events back then (e.g., Jeff Davis’ Secession Speech Jan 1861).
So you have an 1850 Census and an 1870 Census to try to fill in/augment the blanks. I read in some sites that the population increased statistically significantly between 1850 and 1860 (and from 1860 to 1870) I'm assuming due to immigration.
Another factor in reconstructing a true picture is availability of local records. If you drive through a lot of the small county seat towns here in Georgia, in some of the towns you'll see an empty square, others have courthouses built after the war. Marietta is one example. There used to be a courthouse there but Sherman burned it (and the city along with Atlanta and others). The square to this day is empty but for the accouterments of a public park.
http://marietta.patch.com/groups/around-town/p/the-burning-of-marietta
Nonetheless, I think what your analysis boils down to as an average, about 1 in 5 slave owners overall, is probably the most accurate estimate of the ones I've seen.