Writing a non-Christian Book with Biblical Influence

Yes, I really think it's important to implement Christian principles into all the stories that I write.  That's why I try NOT to have feminist heroines, which are VERY annoying anyway.  That is why my heroes are actually manly, not whining little wimps.  That's why the bad guys get punished in a bad way, and the good guys get rewarded.  That's why my children get into serious trouble if they don't listen to their parents, and my older characters are wiser (for the most part) than my young ones.
But, in case you haven't noticed, I am not writing Christian books.  That is, I am not writing books in which characters are Christians (obviously, since I write fantasy set in a different time period!).
HOWEVER, you may have noticed that not every good book is strictly Christian.  And I don't want to write to only Christians.  To use a phrase I learned in English class, I want to write to a "broad, general audience." I want my work to appeal to many people, but I also want it to glorify God.  Is that possible?
Maybe we should look at my current favorite book, A Tale of Two Cities.
I really don't think that Charles Dickens was a saved man, but he certainly exhibited a very Biblical principle in the end of this book.  Sydney Carton, the main character, is despairing about the sacrifice he is about to make until he realizes an important truth:

A trading-boat, with a sail of the softened colour of a dead leaf, then glided into his view, floated by him, and died away. As its silent track in the water disappeared, the prayer that had broken up out of his heart for a merciful consideration of all his poor blindnesses and errors, ended in the words, "I am the resurrection and the life."

Carton gains peace through this great verse, which he repeats several times.  (My overbloated imagination likes to say that he got saved, but I don't know if Dickens really intended for that to happen.)
The point is, in a secular book, the fact that Jesus is the only Savior comes across clearly.  And Dickens books are certainly enduring classics.
Aside from this, there is always the fact that people are influenced by what they read, much as they try to deny it.  If you can put principles directly from the Bible into your writing without saying that it is from the Bible, if you can make the theme of your story moral without directly quoting the Bible, and if you can portray wickedness in the evil light in which it should be portrayed, then you have my great respect.
So much modern fiction today is so dry, and even Christian books, so called, are really Christian in name only.  If we could raise the quality of literature back up to where it was two hundred years ago, when secular books expounded the Bible, then we could, I believe, raise the quality of society itself.
After all, people WILL be influenced by what they read.
So...how should we do it?
First of all, pray that the Lord would bless your endeavors to glorify Him through writing for many people.  Think of a main theme for your story that is directly from the Bible, such as "You reap what you sow," "Children obey your parents," or "Obey them that have the rule over you."  Make certain that the characters in your stories get WHAT THEY DESERVE.  None of this getting away with wrong trash, please and thank you!  It's OK to have characters that are role models, too.  I promise, writing a non-Christian book with a Christian theme is rewarding!
Thanks for reading, and God bless,