...is it possible to use the fact that I am willing to work for cheap to get a job that is better...?
With all due respect, if you were able to do the job better than the university's current faculty members, they would hire you paying full salary.
The reason why most universities set high salaries is precisely to keep the quality of research and education high.
If you really believe you are competitive, then you should signal it to your potential employer. The best way would be with publications. You can also visit the university as a visiting researcher to demonstrate your competence. In any case, dumping the salary is not a good strategy. If salary is indeed irrelevant for you, you can communicate this to your potential employer by stating that you are very passionate about your research/job and you don't care about the salary. There is a whole science behind setting salaries in organizations. Unless this is your field of research, let the university set the salary for you. It is likely to be the same as your colleagues'. Benefits are usually negotiable though.
If you are not that good and don't have enough on your CV to impress your potential employer in the US, go to another country that has lower standards for academia and allows lower salaries.
Edit: Every country I've been to had fixed salaries for employees, at least within one institution. So it really comes down to what country you choose to go to and how highly ranked the university is in that country. But it is HIGHLY unlikely that you will be allowed to work for lower salary doing the same amount of work as others.
If you are not convinced, here is a paper by Akerlof and Yellen (1990) discussing why lower wages for the same amount and quality of work are harmful for organizations. Akerlof is a Nobel laureate and Yellen is the chairwoman of the Federal Reserve.