So the question is: after I orphaned a commit how do I _truly_ make sure it's not visible anywhere on github? Is there no way short of contacting customer support to GC a repo? Shouldn't this just basically be a button on the repo, in the "danger zone" area of the repo maintenance?

Assume you can't, even if you contact support someone will have archived it by the time anything gets done. Murphy's Law of Internet Data Storage applies: if you post something to the internet it'll be public forever; if there's something on the internet you remember seeing once and want to find again it will have link-rotted and been lost forever.