Found successful workaround that is applicable for my scenario:
Don't log off, just lock the session!
Since this script is running on a Domain Controller, I am logging in to the server via the Remote Desktop console and then log off of the server to terminate my session. When setting up the Task in the Task Scheduler, I was using user accounts and local services that did not have access to run in an offline mode, or logon strictly to run a script.
Thanks to some troubleshooting assistance from Cole, I got to thinking about the RunAs function and decided to try and work around the non-functioning logons.
Starting in the Task Scheduler, I deleted my manually created Tasks. Using the new function in Server 2008 R2, I navigated to a 4740 Security Event in the Event Viewer, and used the right-click > Attach Task to this Event... and followed the prompts, pointing to my script on the Action page. After the Task was created, I locked my session and terminated my Remote Desktop Console connection. WIth the profile 'Locked' and not logged off, everything works like it should.