You've received some pretty thorough information so I don't really have much to add to it.
The missing feathers could be from the heavy crop rubbing on perches or the ground. Or the swollen crop could be making the feathers
appear sparse.
I'll address the crop bra because it sounds like it's something you could try. You don't need to sew. You can glue the pieces together. I use a four inch square of sturdy cloth with twelve inch long strips of elastic bandage.
To adjust the bra properly requires monitoring the crop morning and night for several days running. You will know it's properly adjusted when you find the crop completely empty come morning.
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