Quick question, do you know if lds publishers are interested in fictional stories about missionaries?
Of course. Why wouldn't they be? As long as it's well-written and not preachy, has intriguing characters that readers can relate to, an interesting plot line, and upholds LDS beliefs and standards, most LDS publishers will give it a look.
There's even some precedent for interest by national publishers. I know there are some I've heard of recently but Google is not my friend today. The only one I can recall off the top of my head is Charlotte's Rose by A.E. Cannon published by Wendy Lamb Books (imprint of Random House).
[Readers, if you can think of some other titles of fiction with LDS characters published by national publishers, leave the titles in the comments section.]
Just remember, good fiction needs to be good fiction. No one wants a preachy book or a thinly disguised version of the missionary discussions. It has to be real.