Honestly, I think you'd be a perfect fit for BCG Platinion or McKinsey Digital. I'm quite close with someone who came in as a Project Lead at BCG Platinion (i.e. McKinsey EM). This person has done very well for themselves.
MBB would surely love to have you as an experienced hire at the EM/Pl level for their digital/tech practices.
How do you make up for past mistakes? You need to network. In your specific case, reach out to all those contacts you gained from the past 10 years - even though they left MBB they still know people! Ask them to put you in touch
1) Check out the PrepLounge Q&As
2) Sign up with a session with a coach (I can teach you what you need to know in just 1 session)
3) Follow these immediate tips:
a) Reach out to people in your network
b) Reach out to people once removed from your network
c) Reach out to people with a similar backgorund to you (i.e. same alma mater, same historically underrepresented demographic i.e. gender, orientation, ethnicity, etc., same career switch, etc.)
d) Tailor a message to them specifically both showing interest in them and their journey and demonstrating that you have done your research and could be a valuable hire
e) Play "tag" across calls you get so that you can work your way towards the company/office/role you want
f) Never directly ask for a referral, but "hint" at needing one (this is nuanced and important...happy to talk through wording)