Not sure why so many here attack MIA, I've long said people on AA FT go around the airport looking under rocks for things to complain about.

Point of Order: you are conflating concourses with terminals. At MIA there are three terminals: North (Concourse D); Central (Concourses E, F, and G); and South (Concourses H and J). Despite being separate "terminals" Concourses D & E are connected by airside, as are concourses G, H and J.

As others have said, it really isn't worth the hassle. The Admirals Clubs at MIA were and have been overcrowded for years, now that is compounded with the construction/renovation. DL/UA pax come through D concourse all the time to use the American Express Centurion Lounge so assuming they are willing to endure the lines and crowds it is possible.

The best options are either the Avianca Lounge or Delta Sky Club. DL despite not being all that old was recently expanded and renovated.