I usually avoid the self-promoting "hire a coach" answer but for your case, that might be the best way for you to make sure you don't lose out on an opportunity to secure an offer at McKinsey or BCG! I have worked with quite a few experienced consultants (e.g., Oliver Wyman, LEK, Strategy&, etc.), helping them prepare for their McK interviews where they have been pleasantly surprised with how working (successfully) as a consultant doesn't always ensure you are fully prepared to solve cases as well as their misunderstanding on what exactly McKinsey is looking for through the interviews (the WHY is super important).
My personal perspective on case interviews is that it's difficult to "ace" a case as there is always more that can be discussed and refined, just like a client project. The fact that you didn't feel as much of a challenge to me sounds like your interviewer didn't engage with you enough to ensure you really showed your strengths. For example, as a McKinsey interviewer, if I felt a interviewee had strong structuring, I would push them around e.g., the interdpendencies of their structuring which would allow me to have a solid data point to argue your case for why your structuring was exceptional relative to other candidates.
I would be surprised if Bain SEA would turn down a strong and experience consultant target at first round for the reason of quotas. At the very least, they would progress you to final round as they won't just let talent walk out of the front door like that. In terms of feedback, the fact that you have applied through a headhunter removes the hassle of coordinating and communicating with the Bain recruiter but the flip side is that you are further removed from the communication. I wouldn't expect too much unless you really connected with one of your interviewers who out of their own good will is willing to make the effort and invest time in having the 'awkward' conversation with you. If not, the recruiter has only taken down exactly what was discussed by your interviewers when making the decision.
Happy to discuss further if helpful.
