It's called a market. In the situation you describe, you have other offers of work, so you can be strict. How would you behave if you had no other offers? Sure, you can complain all you want about the invoice not getting paid.
Don't be so sure. In the last fifteen months, I've gone from being completely broke to having no debt and about a year's salary in the bank. In my experience, it's much easier to make dispassionate and rational decisions when you're not in imminent danger of losing everything.
This is based on your current "safe" mindset. I can assure you that if you were in a very different financial situation that your thinking would most likely change.
No it's based on me knowing myself very well through critical analysis of myself. I am an all chips in guy. I have been up and down but through it all, I have always been consistent on my principals, when I was starting out I walked out of a really bad position with nary a weeks pay in the bank. I barely landed something new and made the rent in time. Never the less, I stuck to my principals. I made it really big on an exit, bet it all on investments and start-ups, lost it all, went another round after working some jobs, had two good exits and started playing it safer by switching to consulting, irregardless of all of that my core values and principals never wavered. So I am pretty sure, if my financial situation was different, I would still feel the same.
You'd be surprised how one's self can change under unsafe circumstances, despite all the "critical analysis" he had done...
I would put that effort into finding a different job. Tell me that isn't a better use of time.