Initially, I thought about fitting all the different styles into six headings, but after doing an audit of our site, there were a lot more than six heading styles being used. Some were bold, some were light, some were all caps. I decided to split them by size and created folders for them containing the different weights.
I was able to batch create these styles through a plugin called 'Styler'. After creating sizes for the default 'Regular' weight, I duplicated the frame to create 'Light', 'Semibold', and 'Bold' versions. I changed the weights and batch-renamed the text to reflect the weights.