I'd pick th high point for a repeater. One highly directional to hit a (probably AT&T) tower on St.John, and a rebroadcast link down to the main house. Think the cell repeaters have to have their antennas physically spaced apart by >20' to avoid feedback (think of microphones and speakers being too close together. They could also run underground repeaters inside tunnels.
Think of most non-tech billionaires. They don't understand RF and only tell their guys "I want my phone to work all over the island". How many cellphone techs think beyond doing that? This is useful.
Also note the helo pad with the crappy H has a little hut to protect guests from rotor wash.
Is he still active at this island or has he set up shop elsewhere? Doesn't he have some ranch in NM?