What filter are you running in the 10 gallon? Usually works to just put the filter in your main tank when the quarantine is empty. Or depending on the filter, put the media in the filter for your main tank.
I am running just a small HOB filter with a filter bad and some Fluval Bio Max. I had to isolate a couple aggressive fish so I placed a divider in the 10 gallon and let them live in there for a month. They are now back in the 125 and all is well. I want to keep the cycle going in the 10 gallon in case I need to separate any others in the future. I am going to try phantom feeding the tank to see if that works. I also have a Betta in a 5 gallon that I might place in the 10 gallon for awhile. I never stopped to think what I might do with the 10 gallon once I removed my problem children
I have been dosing with 5 drops of ammonia daily and it seems to be keeping the cycle going fine. I realize I will have to do periodic water changes to get rid of my nitrates, but that is a small price to pay for having a tank ready when I may need one for who knows what. You never know when you may need an extra tank ready in this hobby.