In my opinion you should keep the focus on the main problem in hand, which is that the client is not happy. In other words, there is a deviation on how the client expects your product to work, and how it is developed to work (the product team's point of view). Given that your product is huge, there is good chance that the client requirements got gradually misinterpreted down the line of product development process. I would suggest you to identify these deviations from the bug list you have. Another point of destruction can be that the functionalities(or requirements) that have conflicts between them. That leads creation of a buggy application model itself. Something like Alloy may be helpful in that case. The following links from software testing solutions might also be helpful,
https://blog.qasource.com/resources/comparing-a-test-plan-vs-test-strategy-for-software-qa https://blog.qasource.com/resources/enhance-your-software-quality-assurance-and-testing-in-5-steps https://blog.qasource.com/resources/compare-software-testing-methodologies-for-your-needs https://blog.qasource.com/resources/plan-your-software-testing-life-cycle-for-total-coverage
I am employed by QASource.
