Sounds like a case of convergent evolution to me. If you’re going to put a girl in a box, putting her in a fetal position seems a fairly obvious bit of symbolism. The only other choice is flat on her back, which might lead the audience to think “that’s a suspiciously coffin-shaped piece of luggage.” River in the box is a reveal. The position also makes it possible to show a bit of nudity, which makes it even more of a surprise.
As someone who’s never seen Outlaw Star, I’ll take your word on it-- All I know about the comparison is what I’ve seen others say on the Internet.
The fetal-position box is also more compact: You use less material in making it, and it fits in a cargo hold better with a bunch of other mostly-cubical crates. Even aside from being symbolic, it’s practical. Of course, this compactness is the reason why fetuses are in the fetal position to begin with.
As I said, when an image is so very popular, then it’s not surprising to see it come up in lots of different circumstances, including in suspended animation in a box.