I think your suggested solution is a good one. It should be fairly easy to set up one Q2A instance to use single sign-on based on another.
As an experiment, you might even want to try using a MySQL VIEW or MERGE table to share the users and userprofile tables between the two installations. In other words, if your main Q2A site uses the table prefix qa_ and the meta uses qa_meta_, you would set MySQL up to treat any query on qa_meta_users as a query on qa_users, and likewise for qa_userprofile and qa_meta_userprofile.
To be honest, this may or may not work, but if it does, it's easier than writing the single sign-on code!