The EAD Public Interface is not designed for automated access. If it were driven by CGIs then you might be able to screen scrape -- yukky though that is, but it's written with the Java GUI and the security/authentication is incorporated in that. So the best you're going to get is cut-and-paste of output from the GUI. The XML schema are available on the
EAD site library.
If you want real automated system-to-system access you have to investigate the ESI, the EAD Systems Interface.