I'm looking all over the internet trying to find documentation on how to edit already existing document set content types. why on earth does Microsoft make it so hard to find documentation on common things? Drives me nuts. Does anyone know?
Moe's given you some good advice. Here are some links I've found useful on this subject too.
This one is from John White is more detailed and gives some extra ideas including attaching templates to document content types, which is interesting, though not what you've explicitly asked for.
The reason why I could not find or edit that content types settings for the "new" document button for the document set is because those content types were located on a Content Type Publishing HUB. It was there that all edits were easily administered as opposed editing directly on the site's content type's settings which were not available on the site.