One Game Ranch in Namibia that I had the pleasure to stay at while carrying out some culling had done some Elephant control at great cost to themselves. They moved 10 (I think it was) Elephants by road and ship to Congo. This was an experiment to see if it was feasible and if the Elephants would stay there. I must write to them to see what the outcome was.

Nature may well take care of the areas with over populations of Elephant with drought and starvation.
However the two main areas Hwange Nat Park in Zimbabwe and Chobe Nat Park in Botswana have very good water supply, and food supply. That is the Zambeze River and the Nat Park. In time this will lead to these areas being turned into desert. As their sizes decrease, as is happening now due to over grazing by Elephants, either a mass die off due to starvation or the Elephants will spread and more villages will want them shot as they wreck the Villages crops.

A very conservative estimation for Chobe to survive is there needs to be 5000 Elephants a year killed off. That is just to maintain the status quoe. The real number is probably above 10,000 a year to actually reduce the population. Who is going to do that, who is going to pay for it. I dare say, nobody.