One of the types of mosquito that carries zika only needs as much water as a bottle cap. There is no way to remove water to that level. Even leaves can have enough water on them for that.
Spraying is also a bad idea since it is indiscriminate and as you said they reproduce too fast to be effective.
For this problem we should be using genetic engineering. Infertile male mosquitoes would be the most obvious first step. It would dramatically cut the population and it is highly targeted and does not require removing standing water to an impossible level.
There has also been work on RNA based insecticides where the sequence is designed for a particular organism. That technology is too new to use for something like this but in time that would probably be an ideal method to solve this problem.
Lets go with what works and that is using gene drive mosquitoes to destroy the species without harming any other species. No chemicals, no off target effects, no harm to bees and no harm to other mosquito species that don't bite humans. This last one is very important since they will just move into the niche left behind by the species we wipe out and not harm any other species that depend on eating mosquitoes.