Apologies. I really had to think about this.

First, I guess I don't understand why you would need an order in the output. The output bears no resemblence to a graphical org chart. It's all vertical data that most users won't ever see in that form.

The second thing is that if your REALLY need it in a given vertical order, then you can't use EmployeeIDs either as the child or parent ID. Instead, you'd need to predetermine what the order would be according to the graphical org chart and assign a position number to each node. The child and parent IDs would then be based on those positions and you would simply add the information for the employee holding that current position. The good part about that is that it becomes stupid simple to change someone in a position. The bad part is, you have to know what the org chart should look like so that you can assign the positions and the parents of each position.

That's about the only way I can think of doing this without it being by EmployeeID or by Name.