Is there something I'm missing in the Applications and Recruitment Admin menu that will allow me to have email addresses hidden on the Applications?

If not, could there be? At the very least a way to make them hidden to certain ranks and higher, or visible only to the Admin accounts?

Every fourth or fifth application or so I end up getting a message to remove the email from public view, since it makes the application show up when google searching the email address.

I'm afraid there isn't an option for this. The easy solution would be to hide applications altogether from non-logged-in users.

If you head to Admin > Characters and Accounts > Applications and Recruitment, you can edit the applications such that they are only viewable by setting the "Minimum Rank to View" to something above "General Public". That at least hides the application behind a login-wall, shielding the user from search engines and spiders. And if you set it to the lowest rank on your site (that isn't "General Public"), then a user just needs to create an account to view the status/keep tabs on their application.

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It's all in the reflexes.