Ignoring any philosophical debates about whether it is good to work for less: what you are trying to do will be challenging simply because of the way that ordinary academic hiring is done in the U.S. The typical academic "job search" process in the U.S. has at least two "phases". In the earlier of these, a committee of mostly faculty evaluates applications and performs interviews. If this phase is successful, the committee sends a final list of successful candidates to the administration, which makes the job offer and handles the actual negotiations for the job in the later phase. I am leaving out many details here to emphasize that the people who do the interviews are different from the people who negotiate the salary.
Because of this, it is unusual in my experience for the people in the first group to worry about salary at all. For the plan in the question to work, this group would have to look at your application, go to the administration, ask them about it, see whether the administration was willing to go through with the plan, etc. - which would require a lot of effort on their part for just one application. So I don't think you will increase your odds of getting through the normal process by mentioning that you will work for less. The job search process is not designed to handle such requests.
If you really are willing to work for less, and just want to be at a better school, I think you'd have higher odds if you try to bypass that search process entirely. One possibility, if you do not need health insurance, is to contact several departments directly, and see whether they are planning to hire any part-time lecturers or adjuncts, and whether they are interested in having you.
At some schools, these hires are made directly by the departmental administration, without the same formal "search" process. It is perfectly conceivable that a department chair might be able to find a calculus class or two for you to teach, or something like that. I do not think you would get to half a regular salary in this way, and you would probably not have benefits (retirement, health insurance, etc.). But you would likely be able to get some kind of office (maybe shared) and library access.
I am not sure, however, that this kind of plan will really get you what you are looking for, such as desirability of teaching duties. At best, it might give you more time to work on your own projects, or allow you to be in a location you would prefer.