Highly data dependent, but it looks like reverse sorting the keys you want will get the managers in first.

On the other hand, I don't see why you need to have a key in place before you duplicate it as a value. Writing,

my %organization = (
    1234 => '6789',
    1235 => "6790',
    6789 => '6791',
    1236 => '6789',
);
[download]

works fine. If you mean to have values as references to other hash elements, yes, the order matters, but that brings in concerns about circular references also. (Shouldn't be a problem with a proper tree.)