"Since most of the commissioners' hired slaves had been helping masons and carpenters, it might have made sense for private contractors to use them."
Quote from Slave Labor in the Capital, page 150
Leonard Harbaugh began working for the commissioners as a contractor in 1792. He struggled to build the so-called Federal Bridge over Rock Creek. From 1798 through 1800 he built the Treasury building and War office that were beside the White House. He won the contracts by submitting the lowest bid. The payrolls of contractors did not always wind up in the commissioners' records, but Harbaugh usually needed more money and I think for that reason the commissioners examined his payrolls.
Harbaugh came from Baltimore and so was no stranger to slavery. The first payroll below, from October 1798, shows the compensation for the workers of his sub-contractor Samuel Wilson who was in charge of the masons' work. Since this was a brick building, these were likely brick masons, i.e. bricklayers. This was a craft that African Americans had a talent for but, since all the men listed had a first and last name, we have to assume all the men were all free. None of the last names but Wilson match names of slaveholders who hired out slaves to the commissioners. A master named Wilson hired out slaves named Alexander and David. But it is very likely that the Samuel, Thomas, Sr., Thomas, Jr., and Hugh were all related, white and free.
However, there is more to payrolls than just names. The 4th name on the list which looks like "horror cross" to me was paid considerably less than the others. The most likely explanation is that he was a teenager learning the craft. Cross is not on the book's list of slave masters.
Also of interest in payrolls is the list of days worked. The masons put in more days than the laborers which goes against the work plan fostered by the commissioners. They hired a set number of laborers by the year. Wilson evidently tapped a pool of day laborers when he needed them.
In the second payroll for carpentry work, there are only 2 laborers listed, Charles Wolf and Negro Frank. Both were paid at the same rate, 5 shillings a day, which was as much as one of the 9 carpenters on the payroll, Samuel Warring, got. William Warring only got 6 shillings a day. But no one named Warring hired out slaves to the commissioners. Plus calling one worker "Negro Frank" seems to suggest that Harbaugh categorized slaves at least, and perhaps all African American workers, as Negroes.
Given that Negro Frank was given a top wage for a laborer it is likely Harbaugh owned him, but I have not established that yet. He does appear on other payrolls working for Harbaugh.