If it was not clear from your cover letter that you are interested in general management consulting and you didn’t explain how your experience is relevant to this, then I can see why you may not have got through resume screening. This may also be why the HR team is suggesting you look at risk advisory – since they will look at what you have been doing for the last little while and make assumptions on where you fit. HR typically have a narrow brief and a checklist that they are working to when screening.
I think the first thing that you need to be clear on is the type of work that you would like to do. If its related to your current experience (which sounds like an internal audit and monitoring role), then its only the Big 4 accounting firms that would be relevant. They all have teams that focus on this type of work, usually within the Financial Assurance business line (where financial audit typically sits).
If you are looking to do more general operations or strategy consulting, then you have a broader set of options. Again, the Big 4 accounting firms have strategy and operations consulting capabilities, which typically sit in their Business Advisory business line. The top tier (MBB) and tier 2 consulting firms only play in this space.
I think a plan of action might be to speak with risk practitioners and consultants to get a more granular understanding of the day to day work they do. See what resonates with you and get an understanding of the competencies that are required. (Most experts on this site can help on the consulting side). Once you have clarity on this you can revisit your resume and cover letter and refine as needed. Finally to re-engage with the firms you are interested in, since you already have some work experience, try to find a contact in your network or Linked-In that you can meet for a coffee to get a warmer introduction to the firm and get their advice to further refine your cover letter and resume. This will have a much higher probability of access, rather than applying with graduates through HR screening.
Hope this is helpful and feel free to drop me your resume and cover letter if you would like me to review.