*NOTE: This is a workaround, has the potential to result in data loss, and is an unsupported method. If this is not working for you or you lose data, Google or the Help Desk is not able to assist further.*
It is technically possible to transfer a YouTube account from your @ncsu.edu Google account to a personal @gmail.com account, but it is not a supported method from Google nor NC State.
To transfer ownership of a channel, you first have to create an empty brand channel, and then you will be able to move the content from your main NCSU account to the NCSU Brand Account you created. Once the channel is a brand account, you can then add your personal account as a content manager. You can only transfer the ownership after the new account has been a manager for 7 or more days. See the full process from YouTube/Google's documentation here.
Full steps are below: