a) Yes, this makes sense. Depending on how much time you can spend till ~September and how fast you can absorb and implement new knowledge, this is a realistic time-frame in general.
b) No, most likely you cannot circumvent the BCG banning period. Partners can always overall, but based on your previous performance it's unlikely that somebody would take the risk to overrule HR on that (unless you know each other very very well and the partner is really a huge huge fan of you).
c) Withdrawing your application has no impact at all. Instead of appyling generally, networking your way into McKinsey to jump over the CV screening in the first place makes sense, especially in currently turbulent times. For McKinsey specificially, please bear in mind that you also need to prepare the McKinsey PEI in addition, which is a distinct interview format of its own (I wrote an ebook on that single subject, you can find it at https://pei.consulting-case-interviews.com/ in case of interest).
If you need help specifically for your McKinsey application, feel free to message me and we can arrange a session to prepare you for that challenge.
Hope this helps - if so, please be so kind and give it a thumbs-up with the green upvote button!