Answer
Rather than the Attachment Panel's own page, navigate directly to a specific Assistant that happens to share the same underlying client model as the attachment panel (the URL path is something like .../web/assistant/DocReferenceObjectAttachment/CreateDocFromTemplAssistant) and open Page Designer from there — since that assistant shares metadata with the attachment panel, adding a command button to its DocReferenceObjectList list makes that button show up inside the actual Attachment Panel on other pages, even though there's no direct, obvious way to reach that same configuration from the attachment panel's own page.