Early in the season does have advantages as the bush tends to be thicker and so approaches tend to be easier. Restricted water does have an affect, however on Elephants this is minimal as Elephants wont hesitate to walk many many kilometres to available water.
September is warm in Zimbabwe make no mistake, however it is still fairly dry so the heat is bearable. December on the other hand is hot and wet and can be very unpleasant in some areas. Insects are not too much of an issue until the rains come and then there can be swarms of them.
Peronally, I I had to choose a month to hunt elephant for myself in Zim, it would be May. There is still a reasonable amount of water around, certain seasonal fruits are present , and the weather is extremely pleasant. Whichever month you choose, I hope you have a great hunt.