I do have a few ideas, but I'll hold off on proposing solutions at first.
The full edict you are alluding to is:
Do not propose solutions until the problem has been discussed as thoroughly as possible without suggesting any.
So, perhaps while you are waiting to propose solutions, you can actively engage in the prelimaries of exploring the problem. And take a step back, and ask is the problem how to start more social businesses, or is the problem how to reliably fund SIAI and the idea of social businesses is a prematurely proposed solution?
I asked this question for the Q&A:
I also recently asked this of Luke for his feedback post before the Q&A was up, and he mentioned in his response that SI is continuing to grow the Summit brand in a multifarious manner. Luke also asked me for additional social business ideas, citing a lack of staff working on the issue.
Less Wrong's collective intelligence trumps my own, so I'm fielding it to you. I do have a few ideas, but I'll hold off on proposing solutions at first. I find that this is a fascinating and difficult thought experiment in addition to its usefulness both for SI and as practice in recognizing opportunities.
Edited to add: I posted my own ideas concerning SI and social business in the comments. What are yours? Also, addressing some valid points made in the comments, what are some other innovative ways to fund SI?