Hi, @edfryed. There is no way to delete an individual deploy. The only way to delete a deploy is to delete all the deploys by deleting the site itself.
If you need to do this for an existing site, the typical workflow is to make a new site and them move the custom domain from the previous site (to be deleted) to the new site.
Once this is done, the previous site can be deleted. This deletes all deploys for the site in question.
I do see there is a support ticket about this as well. Please do reply either place and we will be happy to provide more information about this issue.