Has CiviCRM ever been through such a process? If not, I would be interested in facilitating this, as I work at the University of Minnesota and have access to this lab.
No, it hasn't.
The National Democratic Institute (NDI) did a bit of less than proper formal usability testing: https://www.nditech.org/blog/2014/08/testing-one-two-three with details of process at https://nditech.org/blog/2014/07/test. Their focus was on their staff using it for their specific purposes, so the results were skewed, and led more to tailoring for their specific needs than general usability improvements (see https://www.nditech.org/demtools/civiparty).
It would be A VERY GOOD THING to get formal usability testing for front end, back end, and admin/configuration workflows and forms. We should conceive of this as an on-going process, rather than a one time initiative if that is possible on your end. We would need to find resources to rework things in response to recommendations. It might be that 5.0 or 5.1 would be a good version to start incorporating feedback.
The Drupal testing was great and was taken very seriously by the core developers, which was essential to getting the resources to really change things for the better. The regret I had was that the testing was limited to what to do with a basic install; reasonable as a start but it didn't end up addressing and thus mobilizing resources to address the problem of staff usability doing daily work with a 'normal' Drupal installation that includes lots of contrib modules. This is a major reason why I am seeing organizations migrating from Drupal to WordPress when they redevelop their websites - the usability for experienced staff during on-going operations.
With CiviCRM the core functionality is much more extensive, and the extension ecosystem not quite as crucial to the daily staff workflows on a typical installation (at least at the moment). So I think it would be more feasible to do testing of representative workflows on core CiviCRM. I don't know enough about usability testing protocols to know how reasonable it is to focus on usability for experienced staff users in addition to the new users and the learning curve they face as either new staff people or as folks just trying to donate or signup or buy a ticket.
THANKS for the offer. Please get in touch with Coleman and Dave about this.
CiviMobile received formal usability testing, but was never really completed as a project. It's referenced in passing here: https://civicrm.org/blogs/petermcandrew/civimobile-where-we-go-here. He gave an overview of the user testing process (which included eye-tracking hardware) at a presentation during the 2011 CiviCon North America sprint.