I ended up finding how to do this. For posterity, you can click the Spine Atlas Asset that is generated by unity when importing and click on the "apply regions as texture sprite slices" button.
This seems to be exactly what I was looking for but I would still prefer to have such an option done automatically if someone knows of one.
Of note however, this doesn't play well with rotations or polygon regions (at least not that I could see) as it seems to be ignoring image rotations and always slices as a rectangle.
