This is a great case where buying cheap fish from the big box store is almost more expensive than paying up for a better specimen with fish husbandry...and more labor intensive...and more lethal... I learned my lesson when I bought 6 fish from Petco and every one of them died from Velvet in less than 2-3 days in my QT tank. I am so glad that you are going through the QT process. Good luck!
So I have concluded that both the FW dip and the copper are stressful enough for it to not want to swim.
Soon after the video above, the fish went on its side and never tried to swim again. A couple of hours ago I decided to pull it out of the copper tank and put it in a small specimen box with fresh SW just to give it a closer inspection one final time. To my surprise, the fish is swimming again... And hasn't stopped. I added a small airstone. I guess if it makes it through the night, I'll move it into its own 10g tank without copper and try every possible food I can think of to see if it will take anything (clamps, mysis, worms, pods, brine shrimp, seaweed...). I still doubt it will make it, but until it's swimming, I'll keep trying.
Time for bed.