We have SharePoint 2013 Enterprise, and we are using the built-in Document ID services. I'm looking for a way with minimal customization that users can easily share documents by Document ID instead of by copying the document's URL. Currently, in the call out menu a URL is displayed that is the absolute URL to a document, and in order to get to the Document ID Link they must go to View Properties. Ideally copying the Document ID's Link would only be one to two clicks all on the same page, instead of the four it takes now over two pages.
maybe i misunderstood the question but it should be a matter of customizing the view and it is more a configuration than a customization.
adding the 'Document ID' field to a view you get a column with a link: the description is the Document ID and the link itself is the url of the record (this is a url like 'http://yoursite/_layouts/15/DocIdRedir.aspx?ID=DocumentIDHere').
the name of the involved fields may be slightly different: i have a localized version of sharepoint and i translated the field names i have on my system.