The PDF requires login information, so I couldn't look at it.
But I think you've made a lot of the same mistakes I have as a bespoke developer:
- Neither party has worked in this kind of relationship before. So neither of you can say, "this is how things are normally done". In such cases, miscommunications and misunderstandings are to be expected.
- You've had to pull teeth to move the client along. It's rarely profitable to pursue such projects. I once spent over a year selling a client on doing a large project, and after all that effort, a new manager sent it to an outsourcing firm in India.
- You're working from specs the client didn't write. I lost $30,000 doing a project like that. You can do a ton of work, and the client can just shrug their shoulders and say, "That wasn't what I wanted."
- The client keeps changing their mind. That's a fast way to lose money on fixed-bid projects - in fact, it's why I quit doing them.
- There are "features [you]'ve already created" that the client hasn't agreed to pay for. Here in the US, that's called "working on spec" - in other words, you do some work and hope somebody will pay you for it. That's fine if you're building nice houses in a hot neighborhood, not so good for bespoke development.
But the real kicker for me is: you and the client have a fundamental disagreement on pricing, and you're almost certainly going to lose. They're willing to pay X, and you think X+Y would be fairer. So you seem to think the choice is between X, or X+Y. But it's not! If your client can just walk away from this project, the choice is really between X, and nothing.
Practically speaking, it's at all not important whether your quote is fair. The real question is whether it's more in your interest to (a) complete the project at whatever price the client is willing to pay, or (b) simply walk away and chalk it all up to experience.
You'll have to answer that for yourselves. If the people in your firm have "day jobs" or otherwise can afford to do all this work for nothing, and having this project in your portfolio would be a real feather in your cap, then it might be worth it. But as somebody who makes his income solely doing bespoke development, and can't afford to take on money-losing projects, this raises so many red flags for me, I'd drop this project like a hot potato.