Living in central Florida and using a (homemade IC) the water from the tap is far to warm to cool wort efficiently after a certain point. What I have done in the past is to cool the wort to 115-120. Then put the carboy in an ice bath. The whole process takes about an hour+.
What I did yesterday is to recirculate ice water after 115 deg. Using this method I was able to cool to pitching temp. in 30 mins. I am sure I can trim that down a bit by being more efficient but it was the 1ST time. What I used was bilge pump from West Marine (about $10.00 it was the cheapest one they had). The bilge pump was fitted with a hose connector so it hooks right up with my IC. Having a boat the DC power supply was easy (battery). I am sure this solution is not for everyone however it worked for me!
(Maybe next summer I will have a prechiller and can eliminate these steps).
I can take a picture but really it is not much to see. Bilge pump about a foot of vinyl hose and a hose fitting.
Actually your method is the one I use and works better (faster) than a prechiller. I pump ice water through the IC after the temp drops to 110 or so. If you want to buy my prechiller I don't use it anymore.
I do the same thing with an old RV water pump hooked up to a 12 volt power supply. I also dump a bunch of salt into the water. This drops the temperature of the water another 5° or so for even faster chilling. Be sure to run plenty of clear water through it afterwards though.