Override default cropping in WordPress for featured images

Is there any way to have cropping happen from the center point in an image? All of my Featured Image uploads are cropped poorly (mostly website screenshots), and I’d love to have those crop instead from top/center for preview versions of the image (such as what would show on index.php [loop] in the theme).

I saw this, but I absolutely hate hacking the core out of fear a WordPress upgrade with cause my changes to vanish. Any recommendations are welcome. I prefer to do this via functions.php if possible, rather than edit my 99% completed theme.

I think the default cropping logic for that image upload spot is center/center, but top/center would be a perfect solution to what I’m attempting to accomplish.