Ok I know this might sound silly but even at 1 week old you can kind of catch behavior and redirect. When you see them biting the other's bill, gently intervene and grab the offender by the bill and look it straight in the eyes and say "No" very firmly. Mine were getting picky on one another and being mean to some of their clutch mates and I was kind of worried about injuries. Within a few days of doing this to the agressors they stopped picking on the other ducklings.
When I got my gosling and put her in with them they were 3 weeks old and she was only 3 days old and they started picking on her and I did the same thing and within a few days they stopped their harrassment.
Just something you might want to consider. If you separate them then they won't be able to be in the same flock but correcting the behavior with a firm "No" and establishing that you are calling the shots seems to actually work. Even today now that they are going on 5 weeks old I can still give them a look and say "No" and they stop what they are doing.