I read cozy and historical mysteries, a bit of Paranormal/UF, and to mix it up, I read science and gardening books on occasion.
As I was going through my books at home, I found these with a full moon on the covers, and thought I'd share.
These are all UF except one cozy. Unfortunately, most them are part of a series, although one is the first (I've noted it below). If you don't mind reading out of order though, these might work for you. All of them should either still be in print or available in ebook.
Note: all of these except the cozy would also work for the Vampires vs. Werewolves square.
First the cozy:
Undeniably Yours by Heather Webber is a cozy mystery with romance. I've read the series, but not this one yet, and it's my choice for the Full Moon square. MC is psychic who finds lost objects; she uses this talent in a roundabout way to find missing people.
Books from the Mercy Thompson series by Patricia Briggs, including the first book,
Charlaine Harris' Sookie Steakhouse series has full moons on the covers of:
3 books from the Chicagoland Vampire series written by Chloe Neill: