If it were me, I would move all the fish to a quarantine tank and keep the live rock in the display. I would treat the fish with either copper or hyposalinity for a few weeks, and leave the display tank fishless for at least 6-8 weeks. This way you could probably eradicate the ich. If you leave the rock wet (unless you isolate it for weeks- fishless), it will keep the ich alive and could infect your fish again in the future, especially when they get stressed. Most people don't like to treat their display with medications, however if you plan on keeping only fish in the future, it should be okay. Just my 2 cents.
