As somebody who would have very slim chances of making it into a prestigious or highly regarded MBA program, would acquiring more work experience in a promising position in Consulting make more sense in terms of furthering my career than going for an MBA in a not-so-prestigious institution? How does one do the math here? What should I be taking into consideration?

A top 100 MBA will typically double your salary in three years. More work experience won't do that. Salary data for major consulting firms are easily available, as are employment reports. Compare the NPV and see where the breakeven point is. If you can't do that, throw $60 at Upwork and get someone in the developing world to run the numbers.