Before I attempt to enlist the illustrator, is there any sense in even trying to publish a work that is similar to already existing material created by another author? (I'm guessing there are other cases where two or more authors have written books in the same series, but I have yet to find an example of such…does anyone know of one?)
The OZ series of books (originally by L. Frank Baum) were continued after Baum's death by various other authors. The original Oz books have also fallen into the public domain, so other authors have written and published books which either continue or reinterpret Baum's original work, even without the permission of anyone connected with Baum's estate.
H.P. Lovecraft's Cthulhu Mythos, Margaret Mitchell's
Gone With the Wind, Gene Roddenberry's
Star Trek series, George Lucas's
Star Wars series, and Robert E. Howard's
Conan series have also been supplemented and continued by other authors, just to cite a few very famous examples.
I think the thing to remember though, is that the works I've identified were produced under license from the rights-holders of those works, since the creation of additional derivative works without a license would constitute copyright infringement.
Now, the basic rule of thumb is that the creation of derivative works without the permission of the rights-holder of a book is copyright infringement. And while you're not necessarily copying the settings, characters, or anything else from the books, you might still find yourself being sued for creating an unauthorized derivative work, since you're obviously trying to copy
something from the original books, what with using similar writing styles, similar themes, the same illustrator, and so on. Without knowing more than just the fact that there's some 'obvious likeness', I don't think a really good guess on infringement could be made, but at the same time, the fact that you're getting a bit of an uneasy feeling about this is pretty telling.
In general, you would probably want to protect your material by registering it with the US Copyright Office, which is a pretty straightforward process, and gives you the most legal protection (you may still have to sue if someone infringes on your rights, but that's a lot better of a proposition with a copyright registration).