So I do 3-gallon AG, but otherwise a similar situation.
The pump sits in a Home Depot bucket in the sink. I run the faucet into the bucket, turn on the pump, and let the chiller dump-out into the sink.
Once the wort had gotten to ~100ºF, I put the chiller’s out back into the bucket and turn off the faucet. The pump->chiller is now essentially a closed loop.
To the bucket I then add ~10 lbs of convenience store party ice. If the ice doesn’t last, I’ll add another 1/2 bag.
Throughout the process I stir the word with the chiller every few minutes. I can usually get to <70 in <20 min.
I have thought about adding salt to get some extra chill, there was a pretty funny thread about this a few years back.
My conclusion was that the cost of the salt is not worth the time improvement, plus running salt water through the pump will seriously shorten its life.
Cheap “road salt” has particulates that will also wear the pump, so you’d want something like pretzel salt or Kosher salt, which is $$$