So I have never dabbled with partial chilling because I do not have a fermentation chamber and my water is cold enough to do the job.
However, I tried something out at one point, to save water, that may be able to be applied. I setup a bilge pump as to recirculate my cooling water for my immersion cooler. This works really well in the winter when I have a lot of snow to keep throwing into my "reservoir" of water (a storage tub).
With that said, if you need to completely cool, you could use your tap water to get as cold as you reasonably can and then switch to the bilge pump solution, adding ice to your recirculating water. Let me know if you want any details on the setup. I can take photos of the pump and hardware.
I have gone from boiling to pitching temp (around 70°) in about 10 or 15 minutes. I have deemed this quite unnecessary, but it can be done.
Another solution is to also put your kettle into a bath of ice water as you use an immersion chiller. If your water is warmer than the desired pitching temp, turn off the water and remove the chiller for your last bit...