Don't take this the wrong way, but what you consider to be valuable experience isn't that impressive in the grand scheme of things. As others here have pointed out, you're in a grey area in terms of your experience. With two years of work experience beneath your belt, you've got just enough experience to think that you're clever, but not enough to actually be useful. Essentially, a strategy house would have to train you as a graduate.
Similarly, you've not yet got enough experience, even with an MBA, to offer the sort of depth that a strat house is looking for. No matter how clever you are, there will always be stronger candidates than a 25-year-old with an MBA. Look around at most MBA recruits into the strat houses -- they're in their late 20s and early 30s. This isn't discrimination based on age (or ability), but rather on experience.
When I was your age, I thought I was the bee's knees. And in a certain sense, I was. Like you, I'd worked hard and achieved recognition for my contributions. I was promoted very quickly. But hindsight has taught me this: all the intellectual firepower in the world, all the creativity, all the energy -- it isn't valuable to clients until you can marry it with real-world experience. And it takes time to get that experience.
Carry on where you are, try to get the best client experience you can, then go do an MBA at a top school in a couple of years. That's your surest route to a career at one of the top strategy houses, if that's what you really want.
