Copied DocumentType invalid

I found an issue when trying to create a new document type by copying from another type using the Document>Copy dropdown in the Document Type configuration screen. When you perform this step, it appears that the copy command fails to update the ‘type’ property on the new document type leaving linkage to the old one. For example,
If I copy ProductCategoryOverview and create a new document type called ProductCategoryTest, the type property under /hippo:namespaces/customer/ProductCategoryTest/editor:templates/default is still set to customer:ProductCategoryOverview, but it should be customer:ProductCategoryTest.

Edit: Please note, client information in paths removed! See linked client-issue for original paths.