Here's your job - perform the work.
Here's their job - deliver the checks.
I would stop work. They have! They have stated that there is a reason that they have not given you your check. The fact that they haven't given you your payment is a good reason that you can no longer continue to give them your hard work.
Look, I know it's not as easy as that at first because you want to work and you want to have work, but it's an unfortunate reality of being in business - people will try to take advantage of you. The only way to win in those situations is to remove yourself from the game they are playing with you.
One of two things will happen: they will decide that it's time to pay you so they can complete the job or they will not pay you and hire someone else to not pay. You have to decide if you trust them, but at this point it looks like they're string you along. The time you spend not getting paid on this job is time you could be pursuing paid work elsewhere.
Whatever you decide to do, best of luck to you and I hope you get your money!
