I was confusing add_image_size with set_post_thumbnail_size. The problem with the latter is that you can only set one ‘thumbnail’ size.
I wanted to be able to keep the original image intact and apply a custom crop to the thumbnail version of the image. I’m using multiple image sizes around the site as the ‘thumbnail’ though.
So the fix here is to change ‘half-size’ to ‘thumbnail’ wherever I want to display the cropped image. It’s a good idea to set ‘thumbnail’ as the largest image you will use it as. Because you will have to use CSS classes to resize it down to the other image size.
There could be some negative drawbacks to this though like when inputting a ‘gallery’ now, I’m likely to get the larger thumbnail image size instead of the standard I had set before.