Will - lots to tackle here. Allow me to make a few statements:
1. Professional qualifications are not highly prized in strategy consulting, so don't get hung up on not getting one from PwC - and similarly don't be fooled that CIMA is going to open up strategy consulting doors that wouldn't otherwise be open to you.
2. It is quite rare (but not unheard of) for consultants to move from a Big 4 firm into a pure strategy house. I would suggest that if joining a Big 4 you should be doing so with a view to moving into their own strategy practices rather than with aspirations of moving to a pure strat firm.
3. Caveat: getting an MBA from a TOP business school could facilitate such a transition, but this would mean not being in strategy consulting for quite a few years - which isn't a great fit with your desire to get into strategy ASAP. It's also a significant financial undertaking for an uncertain outcome - and you'd need to have strong academics to stand a good chance of getting into the top schools that would interest strategy consulting firms.
4. Your best bet at getting into a strategy firm asap would be to apply direct without doing the Masters - if your undergrad grades and university put you in the running for this that is (you don't say)? The Masters could help if it's from somewhere prestigious and on the strategy firms' hit-lists of institutions they hire from; but it will only give an edge to an otherwise credible candidate, it is unlikely to outweigh any deficiencies in your undergrad grades / university.
As a suggestion, try searching on LinkedIn for profiles of people who attended the university you attended and who are now in strategy consulting at the types of firms you would like to join. If it's a well-trodden path you'll see this; if it's not then this should act as a wake-up call and will allow you to assess these Big 4 offers you have received in a different light.
All the best with making the right decision.
Tony Restell
Top-Consultant.com