I'd see if the in-house publicist at your current house recommends anyone. If he/she doesn't, then I kind of think you should do it yourself. If he/she does recommend someone then that not only gives you a person to work with, but it also signals that the in-house PR people are open to working with an outside publicist...Otherwise, I think your best bet is to target reviewers yourself and work with the in-house publicist to get a couple of big name reviews or interviews. My feeling for publicity has always been: the New York Times matters, everything else is nice, but doesn't carry the same weight. If you can't get the Times then the best thing to do is to get as many small outlets as you can - quantity over quality.
Looking at some of your other books, it looks like People or Entertainment Weekly would be really great fits if you were able to get someone to just focus on those two. However, the review queues for those two are as long as the river Nile, so it's a crap shoot.
Based on your strong mainstream reviews, you may want to go out REALLY early and target mystery blogs and people with a following in the business (and do anything you can to get a big-name blurb - your current publisher can do that for you) and try to build up word-of-mouth buzz. That means going out waaay before publication, putting together a snazzy one-sheet, and getting ready to send out 100 or so books. I think you'd do a better job of that than a publicist, and people like it when the author contacts them. It feels more like "I'm helping this human being whose book I love" rather than "I am doing this because a publicist asked me to."
Thanks for the thoughtful response. Actually, everything you advise doing was done by my PR guy at Viking for A DANGEROUS FICTION. Hundreds of books given away, including 100 or so to literary agents, since the book's about an agent and set in the NYC publishing world, and others via Goodreads. All the usual magazines and papers targeted. It hurt that the NYT didn't review, as they'd reviewed earlier books, but it wasn't for lack of trying. The NY Post put it on their "Must Read" list, and an NPR station gave it a rave: big coups, all thanks to my Viking rep. And the reviews were heartwarming.
I'm not complaining. I know a lot of writers would kill to have my "problem." But you know, the goal bars keep moving, and I'm still in the game, trying to score. Thus the idea of an independent publicist to double down on what the publisher does.
The book of mine that sold best and made some bestseller lists was SUSPICION, and that was one that S&S published in a big way. Top-level marketing meetings, money spent on a national radio campaign, personal letters from the publisher to bookstores (remember bookstores?)---all of it paid off big time in sales. The moral may be that to make money, you have to spend money.
As for your other suggestion, acting as my own flack--I don't think I'd ever feel comfortable doing that. Other people can praise my book to the skies to induce reviewers to read; I can't. It's unprofessional, not to mention immodest. I'd also be afraid of being lumped in with self-published writers, most of whom have no choice but to promote themselves. Of course we're all expected to do our bit, and I do: blog, twitter, FB, signings, etc. But I've grown allergic to "Buy my book" pleas from writers, including my own.
Do you have a background in PR? Sounds sort of like it.