That is a pretty big keel on the Coronado 25': CORONADO 25 sailboat specifications and details on sailboatdata.com
which should support the boats weight fairly well.
With a draft of about 3'8" I'd suggest that just anchoring in 4' - 4.5' of water would do the trick to allow you to clean the bottom.
Letting the hull drag in a sandy bottom WILL grind some of the paint off the bottom of the keel. Think: Sandpaper.
You are right though, the tidal range in the FL Keys is pretty small. I'd still shoot for doing this at low tide on a calm day.