The only way to ensure that ich is killed and will not come back is to remove them from the display and treat with either copper or hyposalinity. Since that is not an option for you at this time, you will have to go for controlling ich rather than killing it. Garlic will help. The puffer will eat the shrimp, and they are not cheap, so you may want to skip that idea. There are also reef safe medications that you can buy. They have mixed results. Some people swear by them, others say that they did nothing. You may want to try a garlic/reef safe med combination. Be sure that it is FRESH garlic. Bottled garlic will not do the job. Please read Beth's common treatments FAQ, located at the top of Disease and Treatment, for information on ich and the life cycle, how to prepare fresh garlic and it's uses, and a list of reef safe medications. She also has information about setting up quarantine tanks. They are very simple and not expensive. It is important that you buy one that is an appropriate size for the fish that will be in it and that you allow it to fully cycle.
Your best bet would be to work on controlling the parasites in the tank while you set up a quarantine for actual treatment. If ich is successfully kept at bay then you will still have the QT, should any of them need any other treatment. Most medications cannot be used in the tank. It will also be a good place for you to observe any new fish before they introduce something else to the rest of your tank.