Hi Anonymous,
This depends more on BCG's perspective concerning your performance level, than your own evaluation of it.
Unfortunately it happens that candidates are well prepared and would make excellent consultants, but are just too stressed out during the interviews and still don't get an offer. The uncomfortable truth is that it doesn't matter you well you were prepared and how close you felt to an offer - it's all about what your interviewers see and feel.
Based on your summary it doesn't seem very likely that you can circumvent the 12-24 months waiting period, but in any case it's all just speculation here.
The only reasonable way to proceed is grabbing your phone and calling (yes calling, not emailing...) your HR contact to discuss your individual situation to see if there is any fasttrack possible for you, and what is BCG's perspective on when you can re-apply.
Hope this helps - if so, please be so kind to give it a thumbs-up with the green upvote button below!
Robert
(edited)