Welcome to SatGuys!
AMC 21 puts a very strong signal in the Caribbean for services like Claro Tv.
But the PBS channels are on the North American beam and are weak in your area.
Try locking in one of the Claro TP even though they are scrambled, say 11740 V 30000 peak up your dish, then try for the weaker PBS at 12106 V 2397.
This post is your answer. From Barbary Coast, you may have to program the frequency listed for Claro as number 1 transponder for that satellite; and using this map (above) says you can receive that beam that has it. if you do not have a programmable meter for satellite id; use a dish aimer, and hook her and the wife up to the dish for aiming outside (provide them with tools so they can return), and watch the quality bar inside; and tell them to move the dish until you see quality.
Just kidding...
Using a satellite dish of the sizes you mentioned means the signal should be easy to find. Because the dish must point so high into the sky from your spot on that map, use a straight pole, and a dish that has good elevation markings. That GPS works, so get your exact location, and enter it into one of these AZ/EL number generators for North America, like one found
here; then set the elevation of your dish to the number it gives you; and aim the dish from a perfectly beautifully set straight plumb pole; and aim at the reading it gives you plus or minus compasses magnetic deviation/declination; from behind the dish. Remember, 180 is south; true south a little from that to the west; and the satellite in space farther still to towards the west coast, about 50 degree's (halfway to the horizon) from south and straight up. Also, remember to turn the skew clockwise approx. 15-35 degree's for that satellite, also needs that much twist to register a good signal.
Remember, I do not have your AZ/EL; because I do not have your GPS reading, so the above numbers are only estimated guesses...I just put 11 N and 80 W into the calculator and got these for AMC 21: elevation setting of dish -> 41.1
Azimuth aiming of -> 257 (77 degrees to the west of south)
It is either you get it going, or you need me to vaca in Barbados for you, and aim your dishes; I hear it is nice and warm in the winter there...should have time by December...