Clients with defined ideas and no research to support them

Good Morning.

I recently started a new freelance project that is more open-ended and required substantial research to direct the project. It’s been exciting to focus on design process (feels like a college project), but it made me realize that I’ve been stuck in a rut with too many projects which have started out way too defined for real innovation to happen.

So, how do you present and justify the value of in-depth research? Budget is always a main concern with freelance clients, and the best way I’ve learned to accommodate that is by being very conscious of my hours (research usually gets limited). I’m curious to know the details on how you have navigated through these situations successfully or not.

-Do you pick your battles on projects that have a lot to gain from research vs. those that don’t?
-Do you provide case studies or other proof of value to clients?
-How do you go about letting clients loosen up on their perceived idea of a solution without turning them off to your work?

Thanks for the input.