Is it possible to automatically remix an embed?

Answering my own question. It looks like you can get a remix URL by POSTing to the API.

edit: Unfortunately embedding that remixed URL doesn’t create a new instance for the user. They still have to edit it, which triggers another remix, and then saves the glitch to their account :
I guess iframing https://glitch.com/edit/#!/remix/project-name is the way to go.