I'm batting around 50/50 checking in via phone from east of Culebrita.
It wastes about 2-3 hours sailing (& motoring) the inside passage to EH, calling in, and beating feet back to Culebrita.
You can "cheat" a little by calling in when you pass the sea-buoy, and you might have the call done by the time you get to Dewey, or maybe even before.
The good thing about the Culebrita main anchorage (Bayo Tortugas), is most of the day-trippers leave about 4pm, and if you get back there at 5pm you'll probably have the whole place to yourself.