I don't understand, maybe I'm misinterpreting your position.
Based solely on the scale of the problems yourself presented, you must surely agree that (mega)engineering is the most factible solution in terms of time. Greening the desert might be the best idea but the scale certainly sounds right.
The only solution is to stop releasing CO2. There is nothing else that will save us. How much desert would we need to "green" to compensate the emissions? Where do we find the resources to do so, knowing that we must also cease to emit more CO2?
That's certainly part of the solution, but not the whole picture. Even if you stopped pumping CO2 today, 1) global weather processes have already started,. 2) the rest of the already pumped CO2 is not going to magically dissapear. It will take time, time we don't have.
The only actual solution is to engineer many solutions, supported by reducing the pumping CO2 at a minimum, hopefully zero.
Based solely on the scale of the problems yourself presented, you must surely agree that (mega)engineering is the most factible solution in terms of time. Greening the desert might be the best idea but the scale certainly sounds right.