According to the article Africa: Greening of the Sahara (Claussen et al.), the 'Green Sahara, occurred during the Holocene climatic optimum, occurring at the same time as the "African Humid Period", also similar ages to the events mentioned in your 3rd link. All occurring during the mid Holocene
At the same time in the Amazon region, according to the article Responses of Amazonian ecosystems to climatic
and atmospheric carbon dioxide changes since the
last glacial maximum (Mayle et al. 2004), was
reduced precipitation in the Early–Mid-Holocene (ca. 8000–3600 years ago) caused widespread,
frequent fires in seasonal southern Amazonia, causing increased abundance of drought-tolerant dry forest
taxa and savannahs in ecotonal areas.
Although, this effect was not uniform over the entire Amazonian Basin, the authors conclude from pollen, charcoal and other samples, that the Amazon Basin had far less precipitation (up to 40 less in places), which caused
increased fires and consequently greater ecosystem
disturbance, which would be expected to have caused
structural as well as compositional changes to plant communities,
such as expansion of drought-tolerant lianas and
semi-deciduous taxa within forests and expansion of savannahs
at forest–savannah ecotones. Populations of coldadapted
species (e.g. Podocarpus) were largely eliminated
from the Amazon lowlands during this interval, and cloud
forests on the eastern flanks of the Bolivian Andes diminished
while open, grass-dominated ecosystems expanded.