"white house" may be a "late" mutation.
One version speaks of taking John Henry's body down a "long white road." This could have led to "white house."
I was on a white road this past weekend. It was surfaced with a crushed white rock, perhaps limestone, marble. It was the entrance road to the Francis Biedler Forest, Four Hole Swamp, nortwest of Charleston, SC.
Leeds, AL, is the site of limestone quarries and cement plants. In years past everything around has been covered in white dust. In 1887 perhaps the Dunnavant to Leeds road was surfaced with crushed limestone (I've not been able to check this out).
It was suggested to me that "white road" might itself be a mutation of "wide road." The only argument I have against this is that "wide road" is probably a more common expression than "white road." I would think that mutations in oral transmission probably tend to go from the unusual to the usual. Also, before John Henry's body was taken along the "white road," it was on the "smokey road." The context, therefore, is one in which roads are described by appearance (I think).
Nothing in the Nelson article makes a convincing case.