I thought someone would have done this already.
The vest is easy to remove and is kind of sturdy considering; its the clear plastic backing that makes it sturdy. To remove the vest take off the hands and gauntlets (these look very fragle), pop off the head and remove screws from the back (these go into the figure body, so body replacement will be an issue), remove the back/neck armor (loose at this point), un-velcro the vest (or adjust to tighten), adjust arms and remove vest carefully (the braids are attached and can snag).
I don't think the plates are glued to the vest and backing, think plastic rivets, a plastic post is heated and pressed onto the backing. Each plate is attached like this at 2-4 points. The backing does flex some but wants to hold a straight shape.
Futzing minimizes the blocky-ness but does not seem to eliminate it. Loosening the vest seems to give it a curve at the front but new holes will be needed in the vest for the screws. For me straightening the body and having the belt at the bottom of the vest to hide the gap and make the slight remaining blocky-ness seem more natural.
The blocky-ness seems part due to the solid one piece backing being larger than the armor, and the figure body being too thin; my first thoughts are to trim the backing on the sides closer to the edge of the armor, and maybe trimming the backing between the armor pieces so the armor pieces might "float" on the vest. I am not sure how to do this without cutting the vest or breaking the armor (and of course need to work up the guts to do it), others i am sure will have no problem with it.