Instead of inviting those who would help you achieve your tipping point to an MVP do you need to invite the non influential people? At least until you have your feature set in place?
It's not that I advocate against MVP/Lean Startup - I've been following the movement since it was merely a set of unorganized blog posts. But like all things it's not to be followed blindly and uncritically in a one-size-fits-all manner. There can be real consequences of burning your early users just to prove/disprove theories about your product.