What are our chances of winning a real estate "breach of contract" case?

From the little you've written, it sounds like you breached the contract.  However, that doesn't mean the seller will be awarded damages (they shouldn't get specific performance, since any harm they suffered can be fully redressed by money damages), which depends on whether the value of the property increased or decreased between the date the contract was signed and the date it was breached.  Obviously, if it increased, they lost nothing (other than perhaps some incidental expenses - attorneys' fees, interest on the money you should have paid them, etc.)  and presumably can sell the property for more money now, if they haven't already.