Revision: You can copy from within the diagnostic CLI if you have a data interface configured (either Diagnostic or a regular data interface). I don't know why it wasn't working for me initially (deployment error, maybe).

In 6.3, the FTD copy command doesn't work (https://bst.cloudapps.cisco.com/bugsearch/bug/CSCvn57678), and using copy within the diagnostic CLI doesn't work because it doesn't have any interfaces or routing. So I'm stuck trying to upgrade ROMMON using...