I solved the problem with figure import. My error is obvious in retrospect. All of the troubleshooting was done in LaTeX rather than LyX. I'll post my solution after all 11 of my figures have been successfully imported into my book.
I've successfully typeset Chapters 1 (Introduction) and 15 (Conclusion) of my book using LaTeX in TeXShop on MacOS X. I'm very pleased with the result. If I can successfully typeset my entire book for publication using LaTeX / TeXShop, then I will owe a huge debt to the many people who have contributed to the development of LaTeX and its tools over the years.
I used Dodson's book skeleton as a starting point (
http://www.maths.manchester.ac.uk/~kd/l ... dfbyex.htm) and created my own book skeleton using the memoir document class (many other changes to Dodson's example were also made). I'll post my book skeleton after I get more experience using it.
I figure that if the default settings for the memoir class get me 90% of the way to a satisfactorily-typeset book, then I will be more than happy to dig into the 600+ page memoir documentation to finish the last 10%. So far, this strategy seems to be working.