theory below
i think natsuhi is battlers mom, first thing thats makes me believe that is when beatrice said battler isn't asumu's son, and since there is only 18 people on the island and bernkestel said there won't be anymore than that it makes me believe natsuhi's son is on the island due to the conversation they had, and since erika isn't a guy we can rule her out, and adding to my theory is that it was stated that natsuhi commited a sin 19yrs ago and my theory is that it was adultery so she had an illegitimate child with rudolf and that child happened to be battler.
but what could ruin this theory is the fact that natsuhi's son wanted to ruin her, and i don't see battler as that type of person.
though devils proof should hold up in this, it isnt impossible.
im really proud of myself for coming up with this theory, so pls dont make me feel stupid🥲