Looks pretty interesting, the main selling point for me would be the 'Fully reproducible' feature. I am wondering how you might achieve full reproducibility.
Bite your tongue, wrap up the project gracefully and never work with them again. This is easier said than done, but as you mentioned, you are close to launch and your company could not survive without the deal. Good luck.
However, I would like to point out to things:
1. Client treating YOUR staff poorly is way beyond any line. It should be communicated to the client and explained that it's not helping anyone and that you will be removing your abused staff members from the project, thus slowing the whole thing down.
2. From my past experience, problematic clients have problems paying at the end of the contract. Just make sure this bit is legally covered.