I am a professor of physics and native English speaker. I have written, co-authored, and edited numerous books and academic articles.
I am interested in your project and would be willing to start at your proposed rate, although I would hope that once you see the quality of my work I could negotiate for a higher rate. It partially depends on what you mean by "re-write." I am comfortable with all levels of editing, revision, and writing, from copy editing to original content creation, but that would, of course, affect the rate I would expect if I were to continue with this long-term.