My advice would be to submit it to Proquest (associated with University of Michigan). This is the norm in the US. They maintain a repository of most US theses on microfiche and electronically. There is a nominal charge for independent researchers to get copies of your thesis (you will get very small royalties over time). This database is well abstracted by Google Scholar, Science Citation Index, Chem Abstracts, etc. Can't recall, but there may be a small charge to submit the dissertation and/or a copyright form to fill out.
It is the norm for chapters in theses to be modified slightly and converted into regular journal articles. The Proquest thesis is not considered prior publication by any of the journals/societies I have worked with (Nature, Science, ACS, APS, IEEE, etc.) Just cite the dissertation. (Has tangential benefit of some self-citation...woot!) In fact, I encourage you to convert as much of the thesis into "real articles" because (even though the thesis shows up in Google Scholar) doctoral theses tend to be much less cited/read than "real articles in real journals".
I'm not sure about book publication (many humanities theses are turned into real books by trade presses). So just check on that if you want it before going with the Proquest microfiche. If you just plan to get your own custom-bound volumes, for self/university library, etc., that should be fine...nobody will blink.