“But it isn't hunger that drives millions of armed American Males to forests and hills every autumn, as the high incidence of heart failure among the hunters will prove. Somehow the hunting process has to do with masculinity, but I don't quite know how.”
― John Steinbeck, Travels with Charley: In Search of America
I realize that doesn't mean that they couldn't make your life miserable for quite a while.
It is a shame, your concept sounds like a fun idea.
Your legal defense is "fair use", as a parodical treatment. Which by no means protects you from being sued. As they have already told you they won't grant permission, I think you'd be well served to write something else, or make your work more generic, not specifically tied by reference to Tolkien's work.
Your book sounds very interesting. As I understand it, the dwarves in The Hobbit and LoTR are an allegory for the way Tolkien perceived plight of the Jews.
I'm dirty and ashamed