By default, properties are displayed in the order of creation, however you can sort alphabetically by turning on the Sorted option. Doing this is for display purposes in the Geospatial Administrator and does not actually change the contents of the XML file.
Inserting placement metadata creates the feature's operations and methods. The operations contains the dialog definitions with the properties in the order in which they were created. This is also the order of the properties in the XML file which you can review in any text editor.
To reorder the properties, make a backup copy of your XML and rearrange the properties as needed via a text editor.
Re-open the XML in Geospatial Administrator and insert new placement metadata. This will rebuild the placement dialog with the new property order.
Attached is the XML used to create this content.
Property Order.zip