I can understand feeling a certain amount of guilt about issues making it out to production.  However I personally feel like the overall quality of a product should not be owned by an individual QA but by the entire team instead.  A lot of the "shift left" methodology addresses this.

some of the things that we've done:

*  keep all work small and safe (as possible). 
*  use feature flags
*  BA, QA, SE all agree to basic acceptance criteria before work dev work starts
*  switch to trunk based development 

This would likely take buy in from all stakeholders though.
Good luck.