After looking at some of the other files, I found a solution in how the CMS logs out users from this file: ~\CMSAdminControls\UI\Header.ascx.cs
Around line 563, there is a string on where you want the user to be redirected to from signout, and the function that does the signout process: CMSPage.SignOut(signOutUrl);
This seems to be working much better than the other solution that I found through the articles.