Hi,
It seems to me that you have misunderstood point of
New Document Order setting. This setting is applied ONLY when the new document is created and it means at what position (top, bottom or place as per alphabet) the new document should be placed in the section of content tree where you are adding this document. This means that
NodeOrder (CMS_Tree table) is modified for such document and the document is moved into appropriate position in the content tree section. You can change the position of the document in content tree with UP and DOWN context menu buttons.
If you would change the way documents are ordered (not a problem) in the content tree then the default behavior of Kentico
CMS (UP and DOWN context menu buttons) would lost its point. If you would click on Up/Down button, the document will not move up in the content tree since you removed
NodeOrder ordering.
However, you can see how the documents are ordered in the content tree in
~\CMSModules\Content\Controls\ContentTree.ascx.cs file:
mMapProvider.OrderBy = "NodeOrder ASC, NodeName ASC, NodeAlias ASC";
In other words, we do not recommend you to change the way documents are ordered in the content tree since you would disable then "Up" and "Down" context menu actions.
It makes sense to order documents on live site in your menu navigation web part as you wish, but not to change the behavior or the content tree menu.
Hope this will point you to right direction.
Best regards,
Miro Remias.