I have an extra pump in my system now, so after running hose water through the chiller until I get about 85F, I pump ice water through it to get down lower. I recirculate back to the kettle with a whirlpool until the whole mass is the proper temperature.
Before I had this system, I used to pump wort out of the kettle, into a counter flow chiller (garden hose attached), into 20 feet of copper tubing in an ice bath, then into fermenters. This worked fine, even in Florida. It works best if you move the copper tubing around in the ice bath or stir the ice-water.