Wanting to get into M Consulting- Looking for the right firm/role

I'm currently in sales at a SaaS company and have been looking to make a career change into (Management) Consulting. Through my research, it seems that there are a lot of subcategories under the "Management" Consulting umbrella, between which the definition/relevance of management consulting seems to be blurred.

I've been looking at a lot of different firms and positions, some of which do a good job of describing the roles/ specialties explored within the role, some not so much. I'm hoping to get some context on the type of firm/ position that would align with what I'm looking for in a consulting career.

My ideal role would involve creative problem solving for broad business issues. [As an example; a client that makes VR headsets and is trying to increase user adoption. Finding a solution such as converting their product to a subscription model + aiming to form partnerships with developers to increase quality/ utility of their VR game offerings.] [Another example: A company with a mobile app is looking to increase their userbase. Recommending changes to design/UI to simplify functions + rebranding to address a new, more exploitable market.]- These are both examples of the types of problems/ solutions that would interest me in a consulting career.

I have a positive vision of Design/Creative consulting in terms of brand, marketing, product, etc., however I'm not sure if this specialty is as well compensated as others and if it is too specialized to provide a wide breadth of lateral opportunities down the road. I think the ideal role would involve problem solving using a blend of rebranding/redesign, strategy changes, marketing changes, etc.

I've seen openings at firms that seem to fit this mold; however a lot of them will specialize in a few industries (ex: Capgemini [Invent] seemed to focus on consumer products, retail, auto, life sciences and financial) which is undesirable as I'm hoping to get as much exposure in different fields as possible.

To summarize, I'm looking for a position where I can solve a wide array of business problems through a wide array of creative, out-of-the-box solutions (rebranding, design, strategy, etc.) at a firm that services a wide variety of clients (not just sticking to a few target industries). From your experience, what roles/ firms fit this description?