I have been working with OpenGTS and GTS Enterprise (GTSE) for about 3 years.
Several months ago I was in the process of integrating OpenGTS and Wordpress with the intention of using Wordpress as the front end / UI Using Wordpress as a front end also has another advantage in that there is a shopping cart plug in for Wordpress that supports subscription sales.
Anyway it is possible to modify OpenGTS to use the User table in Wordpress and handle the password encryption the same way Wordpress does. It would the be just a mater of using cURL to talk to the OpenGTS installation from within Wordpress, then use the HTML & Javascript returned by cURL to populate parts of the Wordpress pages.
You may want to rethink the UI described in the image you posted. Some functions are missing, and there are functions described that do not exist in OpenGTS.
Please contact me if you have any questions or other requirements.