I did exactly this: joined McKinsey as an experienced hire (6 years), no MBA, coming from a digital product and GTM background. So a couple fo practical things: you still come in as an associate and you still learn the consulting craft from the ground up, and you don't storytell your way into a general application.
Seniority doesn't buy you past that. What it can change is your staffing pool. I joined as an integrative associate tied to a practice, which meant the projects I got pulled onto were built around my expertise, not my office. So at your level the question isn't which office, it's which capability do I map to. For McK I'd say Growth, Marketing & Sales and/or Digital, I'm sure there are Bain and BCG equivalents.
So I'd recommend you apply into the practice, talk to the partners who own that capability, and frame your story as commercial impact you shaped.
One more thing: experienced hires still get pattern-matched hard in the case, and your seniority raises the bar rather than lowering it. It is an advantage for the fit piece though, you will have real stories most recent grads don't.
Happy to go deeper on positioning or the overall process as an experienced hire if useful.
