Seems like as far as civilian bodies go, it's access to ST tech that's the choke point. There's billions of Yamataians on thousands of worlds and even more spaceships, some of whom take some very big risks. It seems implausible that there wouldn't be at least hundreds of disappearances where they're presumed dead and revived back home without the body ever being recovered. The hard part would be getting those bodies to customers, since I'm pretty sure ST tech is strictly regulated for a billion reasons.
Stealing bodies from soldiers would be a lot harder than going after joyriders, pirate poseurs, extreme xenomountaineers, and the like, for the very same reason that soldiers aren't able to do those things even if they want to--there's a lot of people keeping an eye on them, and they take things seriously.
Maybe Yamatai keeps an eye on everyone, though, I don't know.