It really depends on what you want. Assuming you just want a finished product, I'd set up frequent calls/meetings with the company, even as frequent as daily. I would ask for daily updates listing what was completed today. I would push for frequent deployments to a staging/user acceptance environment so that you can see the progress being made. They may push back on you when you ask for this, but if they are 2 month overdue on a 3 month project, I think you are completely within you rights to expect them to provide you this sort of involvement.
Knowing that you are taking an active role in getting the project finished will most likely make a significant difference.
The other approach is to contact a lawyer and see if you can get your money back and start with someone else. If you really think this contract is dead, then do this, but the pain in this is obvious. This is a startup discussion, so I assume more than anything you want the contracting company to complete the project as quickly as possible.