An MBA can absolutely create a cleaner recruiting entry point for this kind of pivot. Campus MBA recruiting is designed to bring in candidates from many different pre-MBA backgrounds, so you would not be expected to have spent the previous several years doing strategy consulting.
The tax background is not automatically a problem. What matters is whether you can translate the experience into skills that are relevant to consulting: client management, analytical problem solving, leadership, working through complex regulations or business decisions, and delivering under pressure. The MBA then gives you a structured way to add broader business exposure and recruit through a standard channel.
I would not choose an MBA solely because you believe it guarantees MBB. It does not. School placement strength, your overall profile, networking, and interview performance will still matter a lot. But if the MBA also makes sense for your broader career goals, it can be a very credible way to reposition yourself.
Before committing, look closely at the consulting placement data for the schools you are considering and talk to recent students who entered MBB from nontraditional backgrounds. That will tell you much more than trying to judge your odds from the tax title alone. A useful reference is how MBB and Big 4 differ if you want to go deeper on that part.