Who should own the staging database right
You say 


  however we're blocked again and need to make another ticket to have
  our SQL run in the production environment.


Why? This should surely all be part of one ticket - bug xyz.

What I would do is have the original developer push it out to production and the original tester repeat their tests on the production system (or get the client to do it) and verify that the results are a) bug-free and b) work as the original tester saw fit to pass.

What bug-tracking software are you using? I thought that most of them (all) would consider deployment part of the process for one bug-fix - or that they would allow you configure your system to make that the default behaviour?