You could add a new field to each custom type (node-type) and use a constraint with just one value, the node type. Or add a rule that would set the value of the node-type field whenever an object of that type is created. Then display the new node-type field in the details page.
If you add a new property to your custom type, for example node-type, then you could use nodeService setProperty (or setProperties) to update that field. Then display the field in the "Show Details" page.