I hear ya, I'm in the same boat here. We have a solid foot thick layer of calcium carbonate rock / rubble (from canal digging) with a 3 - 4 inch layer of sand on top.
Honestly, a lot of soils repel water when dry. Peat is especially bad, but even compost does it. The key is to keep it watered during establishment or wait until the summer rains kick in. Best time to plant a mango tree here is August, since you get the summer rains, and mangoes naturally lay down roots during the fall (the yearly cycle is roughly: dormant => fruit => grow limbs => grow roots).
To repair chlorosis, sulfur helps a lot in that it temporarily drops pH. As an experiment, I dropped the pH of 1/4 acre of land from mid to high 7's to the 3's with a literal ton of sulfur. Took a good 5 years for the pH to return to the 7's. (PS -- you can buy OMRI listed sulfur pellets if that's something you're interested in.)
Also, consistently apply micronutrients (Tiger produces some good ORMI listed micros, and conventionals are easy to obtain). Consistent foliar application helps too.
Re :Compost
My soil in Cape Coral is so poor that I HAVE to fill the planting hole with topsoil/compost. The topsoil in my neighborhood is really subsoil from canal excavation used to elevate the residential lots. It is sand with shells/coral rock of various sizes and almost no organic matter or life. I have no irrigation system and the well water is very salty.
When the top layer of ground dries it actually repels water. Almost everything goes chlorotic so I use a lot of liquid iron and similar granular products. I would use soluble kelp powder if it wasn't near $500 a pail.
Once the soil is dry even a heavy rainfall will only wet the top inch or so and then it is dry as dust beneath.My first mangos were planted by the book. All struggled and most died. Filling the planting hole with compost has greatly increased survival.Sometimes I give the trees a little molasses,it seems to help.
I have to fill the planting hole with compost and at least a 2 inch layer of compost surrounding the tree so I can successfully water from a can or hose from my Reverse osmosis system. If there is some moisture the soil drains fine. When dry, water just beads up and runs off.
Once mangos are established I try to give them a little water around bloom to minimize fruit drop. Last year I was unable to water. The trees set a good crop but the rains came so late much of it dropped. Mature mangos do fine in the neighborhood but young trees struggle. The past two Winters it has hardy rained at all.
