I'm a little self-conscious about this novel in particular
Have you had work critiqued before? It might seem worrying at first, but there's really no harm in finding out what problems might lie in wait.
Honestly, I wouldn't want randoms critiquing work in private if I was very self-conscious about a piece. Mostly due to there's no regulation with what people can say in private, and often due to that people can step out of line or suggest completely incorrect things. With an open forum like the SYW section, critics have to be more careful and make sure what they are saying is correct because of public view. Critics can also correct others (I have on occasion), and disagree with one another--but in that you can get differing view points and ideas. Work that you're self-conscious about is best, IMHO, to be handled by critique buddies or trusted beta-readers that are willing to put up with some rough work. Since you're asking the general public, I don't expect you to have those.
I'd still suggest the SYW section. Start a post stating it's an unconventional/experimental writing style you'd like feedback on. If you're worried about harshness or people hitting on certain aspects, you can suggest they soften their critiques a bit (although don't ask for too much, and you can't fully control what people say). Critters are an understanding bunch.