" near no name key and big pine key on the west side,"
on the west side of which one? Neither looks good for dropping a hook unless you have a hovercraft. If you have the NOAA
charts, you're looking at channels on the south side of the highway and extreme shoals on the north. Anchoring in a designated channel should get you a quick USCG visit. Getting stuck in the shoals...might not be any more fun. There are some spots NE and NW of NoName that might do though.
You may only draw three feet, but once you park those twin keels, you're not going anywhere, are you?