BARGAIN! ONE USED PRIME MINISTER.
Don't be fooled by the patina of age. This classic model has plenty of mileage left on its clock and could easily be re-purposed as a combined swimwear model and budgerigar relocation system. Versatility guaranteed.
GOING CHEAP! Don't miss out.
Sold as is. Warranty not included.
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