Soo first of all, I don't think you are at any disadvantages at all! Not regarding the funding and not regarding the recommenders. You just need to explore other horizons and other ways of approaching the application.
Soo, first of all, having started a non-profit probably puts you in a BETTER position than most of the people who have just moved up through corporate. Of course a lot depends on the non-profit itself, its size, its fundraising, your results, etc. But if those are good you could potentially have an amazingly strong profile.
Regarding the recommenders, there is no disadvantage here, although it can be "tricky". The first thing you need to do is to explain yourself in your optional essay (i.e. write "I have always been self employed...") Your recommenders could be pulled from clients, partners, academic advisors/professors, supervisors in other capacities (in volunteer work, social or religious life) etc. Whatever the case you definitely somewhere in your background have three people who would be great recommenders. Figuring out WHICH to choose is the hard part though!
Finally, regarding the "unfairness" of sponsorship. There's first of all nothing unfair about it at all. Huge companies with huge funds invest in their future. It's only natural. Secondly, outside of EMBA programs this happens much much more rarely than you would think. Thirdly (and most interesting for you) if you are in non-profit there are all sorts of "Tuition forgiveness" schemes and special scholarships (both from the schools and from outside institutions). Look for example at Yale:
https://mba.yale.edu/MBA/admissions/fina ... ness.shtmlYour recommendations will NOT disqualify you!! You have potential to be a very strong candidate, you just need to "choose wisely".