Generative research – methods for finding areas of improvement in an existing app

I'm frankly surprised by the lack of questions on here about generative research. This is the tenth question ever posted here about it.

Regardless, I'm finding myself at an impasse in approaching research for businesses who just ask me point blank "Find problems and make it better." Surveys can be helpful but they're better when I have some basis upon which to write the questions, otherwise I may just end up validating my assumptions. I don't like the idea of doing my own heuristic analysis because again, I'm just testing my own personal biases and not inquiring on behalf of the user. Most businesses don't like the idea of having to shell out the money for lab tests/contextual inquiries right away because they feel there's no guarantee in their mind that I'll identify valid areas of concern based off of 5 or so user interviews. Which is more a testament to my ability to communicate the value of UX rather than the method.

This has been a sticking point for me and I'm ready to fix my problem. What are better ways to not only conduct generative research to identify areas of concern that involve the user, and is generally going to be well received by the product owner? Thanks.

I suppose with existing products it may be an idea to just look into evaluative research methods but I would like to include generative as well.