R.W.
Maybe your neighbors have standing water? That is how they breed and they don't live very long, so there must be some water around.
Maybe the spiders are eating the mosquitoes, and that is why there are so many spiders--lots of food for them. If the mosquitoes go, the spiders may go to. In the meantime, are you able to spray your plants with a hose? If you do that frequently, I think the spiders will find somewhere else to make a web.