Those fertilizers are probably better than 20-20-20, but notice that 7+5 = 12% Nitrogen , which is high for mango, versus 3 + 1 = 4% Potassium, which is extremely low[assuming you used equal amounts of each of the two products]. The middle number, Phosphate, is O.K.
Yes, root-pruning, then placement into a plain sand hole, leaving a berm to hold water, is what is generally advocated for mangos.
I often add a little Calcium Sulfate and a little "organic" fertilizer containing Mycorrhizae and beneficial soil bacteria. I haven't proved that there is a benefit.
Beyond the water-retention berm, in the 3-foot radius where sod has been removed, I add about an inch of light garden soil (Lambert's), place conventional slow release fertilizer and organic fertilizer over the garden soil, and cover with mulch. This makes an instant topsoil over the sand, favoring mango feeder roots there.