You don't need a lawyer pro-bono, just one on contingency. If you can survive the motion to dismiss at the outset, you've now entered discovery, and BigCo will now start incurring bigtime legal costs. Settlement offers will be forthcoming. Litigation isn't about winning in the courtroom, it's about inflicting pain until someone says "uncle". (Patent litigation often goes further because the stakes are so high. Your five-figure breach of contract suit, not so much.)