I would be wary of giving very much credence to any of the Moorjani et al conclusions. All of the figures for West African admixture are inflated. The Reich lab which produced it corrected the assumptions upon which their calculations were based in their subsequent papers, including, of course, Lipson et al. I think I already posted this somewhere. If you want to see the detail of the problems with Moorjani et al just search on Dienekes site. He pointed them out as soon as the paper came out, and the subsequent Reich Lab papers took exactly the same approach as he had advocated in his blog.
Also, in some cases, although not in all, the program used to date the admixture seems to have problems differentiating between the general time of the most recent admixture and the cumulative effect of all the prior admixture. In other words, let's assume that in a certain area, there has been admixture for two thousand years. The program might, depending on the population history of the particular area, pick up the last date of admixture as the only one which occurred.
An example of how the program might give erroneous conclusions is in the case of the Egyptians. If I remember correctly, the admixture with SSA was held to have occurred in the late classical era. That defies logic, in my opinion. While I'm sure that the Arab slave trade of the slightly later Arab/Muslim expansion greatly impacted Egypt, it seems pretty obvious to me from archaeology and the art of prior periods that there was SSA admixture before then.