I finally finished my new chiller project. Before I was using a 25 foot copper coil, but I've wanted to do in-keg chilling for a while. I ordered a longer version of what distillers often use and sat on it for a while as I decided how to deal with the water supply in my new apartment.
I eventually got around to replacing my water supply line in the bathroom with a 2-output supply, and added a quick-disconnect so that I could easily hook up the chiller.
After this, I was ready to chill in the keg without much issue. I dump my hot wort into a keg to ferment in, and my sanitized chiller gets to work.
I'm able to chill with the keg in the shower, and if I want I can put the output of hot water directly into the laundry machine.