You are concerned with the logon and Logon2 hidden fields information if it is needed when using EZproxy and RemoteAuth Authentication.
Yes, they are necessary for the Web Pages, but not for EZproxy. When you are using EZproxy to authenticate, the patron never sees the Logon or the Logon2.html web pages. You authenticate the patron directly to your EZproxy. Then you forward the patron to the ILLiad.dll page. Because you are sending the patron information over, ILLiad will send the patron to the appropriate page.
Please see the attached document on Integrating ILLiad with EZproxy.