sudo: unable to cache user root, already exists
It seems that in my case I was able to repair the problem while writing my question, by reading the man pages more closely and running the following command:

sudo -k


This command revokes all outstanding sudo permissions and forces you to re-enter your password the next time that sudo is used.

However, I've been unable to discover why this issue presented itself in the first place, but wanted to post my solution nonetheless for the benefit of anyone else that encounters this problem. If someone knows why it might happen then please feel free to comment or add to this answer!