If I were you, I'd probably pick one set of parents for now, until you know any better. Use the notes or an event to explain your doubts, so there's a record to remind you of where you've been before. Use the AKAs to record the variations in surnames you come across.
If/when you find that the parents you chose are the wrong ones, you can unlink the kids from those parents and link them to the right ones.
Or, you can attach all people you suspect as parents and document why you have done that. A person can have more than one set of parents - ask if you need help with that.
Hope this helps. :-)