I've previously posted here about integrating with Joomla. My previous posts have gone some way toward a solution, but I have now done more work on this, and have a much more complete solution.
The solution comes in the form of a Joomla extension, which you can download from here: https://github.com/SFWLtd/plg_q2a_integration
. This extension includes a Q2A single-sign-on file, which links directly into the Joomla extension to check user permissions.
(I've also submitted the extension to the Joomla Extensions Directory, though it is currently still pending acceptance there, so no link yet)
This solution is now in use on a live site to provide a private-access Q&A board, and it is working well. If anyone else wants to use it, please download it from the Github link above and follow the installation instructions.
I would like to make one further point, however: I feel this integration would be even better if Q2A could link to it automatically. Q2A already has Wordpress integration by setting a flag in the config file; a similar flag for Joomla could be added to tell Q2A to look for this Joomla extension. Would the Q2A developers be prepared to accept such a patch if I submitted it via github? Thanks.