Fix for when Photoshop's "PhotoMerge" doesn't work
I'm not sure if this would work every time, but it worked wonders for this image that wouldn't work. I will be trying this with more images and update this post.
I put some dots on the images in approximately the same places. Then saved them individually and opened them up together again using Photomerge, which did a great job of merging.
Best to put the dots in places where they will be easy to remove with the clone stamp tool.