As mentioned, leathers are super resilient. Zoas and a leather were some of the first corals I added, so I think it will survive. They shed (peel their skin) when growing, so that slime that you see coming off is either from growth or stress and I'm sure it will recover. Drop in a small bottle of Dr. Tim's to drop that ammonia, water change, add an ammonia binder and then water change, any of these should help.
I wouldn't get discouraged over the change to a reef aquarium, I think everyone goes through this. You did buy some hardy corals, so I'd say give them a moment to adjust. I think making changes quickly will stress them out more, they are already in your tank and may have to adjust. As a quick note, Reef Crystals have a high alkalinity, which will be hard to adjust to from most shops that you might purchase corals from.