For those panels across the abdomen, you could use blue camp pad foam (it's just a little bit thicker than craft foam, so I think it'd look more like armor), wrapped in a tight fitting bag sewn up from black cotton duck.

This is a piece from my ODST soft armor, which shows how it looks. One thing I'd recommend is using a spray glue to glue the front piece of cloth down to he foam. If the parts get much above 4x4 inches, the cloth will pull away from the foam a little, and look goofy.
This is a piece from my ODST soft armor, which shows how it looks. One thing I'd recommend is using a spray glue to glue the front piece of cloth down to he foam. If the parts get much above 4x4 inches, the cloth will pull away from the foam a little, and look goofy.