I was ready to finish up this project.
I wrapped the Teflon tape around the threads of the new valve and screwed it in the copper pipe. I tightened it down and made sure the outlet of the valve was in the same location as before. I went downstairs and turned the water on again to check for leaks. There was none to be seen, so it was time to put everything back together.
I got the laundry sink cabinet back in place first. I had to shut off the water to install the water lines for the sink. Once I installed the water lines, I attached the washer lines to the shutoff valves. Hopefully, this was the last time I would turn the water back on for this project. Back upstairs to check for leaks again. So far, so good!
I reattached the waste pipes to the laundry tub. I filled the tub with water, checked for leaks and found none. Before I put things back under the cabinet and re-install the cabinet door I would wait for a few hours and check again for any leaks. I had time for another DIY project!
Later that day, I reached under the cabinet and felt around for any signs of water. With a sigh of relief, I sat at the dinette table and enjoyed my success with this project. A Zen moment, undeniably.