I have only eaten a few but......
The old trick with a lime and lemon is to roll it hard 10x against a kitchen surface. Then squeeze the juice out. Prolly youtube videos on this.
Here are the steps for a juice mango, My thinking at least.
At room temperature
Or warmed up by the sun
Roll juice mango 10 times hard on a kitchen surface. Maybe 20 times
Refrigerate and let it get nice and cold
Remove it.
Now do it your way to get the juice out
It is well known that by refrigerating vegs and apples, that it is much easier, you can extract more juice than if done with veg/fruits that are at room temperature