In this day and age, with more and more people going the self-publishing route, I'd be interested in experiences from/opinions about how to go about having your self-published book properly peer-reviewed.
I think "peer reviewed" and "self-published" don't go together. You get a piece peer reviewed to provide and objective, 3rd personal appraisal of the work. You self-publish because you couldn't get published anywhere else. Everyone will automatically assume that your book wasn't good enough to get published somewhere "real" if you self-publish.
Some quick comments to explain my remarks above. They aren't intended as normative remarks (i.e. "Nobody should take a self-published work seriously") but rather as descriptive (i.e. "Whether it's right or wrong, people aren't going to take self-published work seriously.") Sure there might be exceptions, but I think it holds up as a general rule. Here's the reasoning behind that descriptive claim.
The reason to publish is to disseminate your ideas. You don't publish things intending for no one to read them. Therefore, readers and other evaluators of your work, like tenure committees, grant agencies, etc will assume that you are publishing your work in the "best" places you can, i.e. the journals that are read or cited the most or with the publishing house with the best reputation in your field that you could get published in.
There are two reason for peer-review. First, the criticism of informed peers helps improve the work. Second, because the peer review process provides an independent evaluation of the quality of the work. Peer review has a signaling function within the academic community--it says that you aren't a crank. This second function is hugely important. There is too much to read and cranks are always pushing new nonsense all the time. Nobody has the time to sit down and give a careful, thoughtful evaluation of every piece that appears relevant to their research question, so they use heuristics to sift out the nonsense. Peer review is one of those heuristic filters.
Now, if you already have an established academic reputation, maybe you can get a readership without the peer-review heuristic based on your prior work. But then you'll be missing out on the other benefit of the peer-review process, namely the helpful criticism of your peers and an objective 3rd personal appraisal of the strengths and weaknesses of your work by an editor. You could hypothetically get your friends or acquaintances to review your work, but (i) given the time constraints most faculty face, I think it'd be hard to recruit quality referees for your self-published work; (ii) their reviews won't be blind; (iii) there won't be an independent 3rd party editor who makes the final call based on these reports. If you are self-publishing you are the editor and the author, hence you have a conflict of interest and can't give an objective evaluation of your own work.