So we decided to raise the coop on posts and see if this helped. Our initial plan was to raise it up, put chicken wire around the entire coop, and keep the chickens inside the coop for half the day. But, I don't want to keep them cooped up. They seem to really love free ranging all day :) So, we just raised the coop on posts.
A few 4x4 posts, four 2x4 boards for support, some cement, and a bit of paint, and we had the base ready. The moment the coop was raised up, the girls came to find out what was going on. Once we added some hay inside the nesting boxes, they started laying eggs in the coop. And, mongoose have not been able to get in because the nest box access is about 5 feet off the ground. Success!
The coop is also now in a really shaded area and the girls really seem to like hanging out around it now. Doesn't it look like a cute little house now? I like it :)