You need to stop setting a time limit on the cycle, it will be ready after the nitrites go to 0 and not before.
Never put copper in your main tank. I would suggest that you setup a QT tank and go ahead and get your fish in there as they will need to be QT's for 6 weeks or so to make sure they have no diseases. You also NEVER treat anything without it being an issue, do not treat copper just because. It's very stressful on most fish and can actually kill others.
The only thing you should be doing now is waiting for the nitrites to go to 0. This will happen all of a sudden. Then you should wait a week of 0 ammonia and 0 nitrites before you do anything, then when that time comes, and it will, you do a large water change to drop your nitrates... Now you can add fish, so the ones in quarantine will be ready to switch tanks,
I just read your post again and realized you were talking about a QT. Yeah you can use Prime to drop the nitrites and to keep ammonia at 0. I would get an ammonia badge as it will tell you with color change that you have ammonia. Much easier than doing the full test.