Sounds like you have a problem.
Personally, I would never indulge in what MoD call a 'Cost Plus' job where the developer gets a monthly payment - regardless.
When I have done one or two odd IT jobs, I have always worked on the basis of a fixed price with a percentage up front and the balance on acceptance. Customer invoked changes *had* to be negotiated at the time of request because a seemingly simple request might mean undoing a lot of back-tracking (rather like chancing the colour of the bricks in the foundation when the house has reached weather tight).
With something that could be so expensive, cut your costs and get a solicitor (one who understands these sort of contracts) involved. It will cost; but could save money and problems at a later date.