An interesting paper, have you thought about tying it to the Younger Dryas Event?

You are basically discussing the period directly after the YD as temperatures climbed back to the Holocene Optimum that you describe. A period that was about +1.0°C warmer than the climate of the late 19th century.

Starting around 5,000ya temperatures have been slowly declining. Between 1950 and 1980 we warmed the earth back to the Holocene Optimum and reversed 5,000 years of cooling in 100 years of rapid warming.

CO2 levels didn't go down during the YD. The cooling was a forcing that over rode the CO2 forcing. As that forcing dissipated the CO2 forcing reasserted itself and period of rapid cooling was followed by an extremely rapid period of warming.

Stabilizing with your "Green Sahara" period. Which persisted for thousands of years. Well into the Egyptian Era. There are records of estates being abandoned to the expanding desert over the centuries.

So, was the Green Sahara a product of the YD or would it have happened anyway as a result of CO2 warming and the normal interglacial climate activity?

Sadly, we have blown so far past the CO2 levels and temperatures of the Holocene that "what comes next" is uncertain.