This answer which you link does in fact have almost the solution.
The key resides in the ItemPanelTemplate HorizontalAlignement property!
<Menu HorizontalAlignment="Stretch" VerticalAlignment="Top">
<Menu.ItemsPanel>
<ItemsPanelTemplate>
<DockPanel HorizontalAlignment="Right"/>
</ItemsPanelTemplate>
</Menu.ItemsPanel>
<MenuItem Header="File"/>
<MenuItem Header="Edit"/>
</Menu>
However, if you indeed want 2 or mores items to the left AND to the right, you will need some hacky solutions like this one, which requires the number of items to be constant.