I expect that the primary challenge you face is one of differentiation in the job market. There are a lot of independent consultants and "coaches" out there, and quality tends to be low, so you need to stand out from the crowd.
The difficulty lies in moving from a very personal, networked approach to getting work, towards a more professional, rigorous and disciplined approach. These are the types of things you might look to emphasise in your applications.
That's not to say that "corporate" consulting is any less incestuous in the way contracts are awarded, but you need to demonstrate to potential employers that you can change "families" and be credible with their clients. This is where a degree, or particular business school background, or professional qualification comes in, so this is where you need to demonstrate equivalent strength in your applications.