As indicated here, I tried installing the CKEditor plugin to see if a different editor would work. I disabled TinyMCE Advanced first, then I was able to install and verify proper functionality of the CKEditor plugin without having to perform a browser reset or cache-clear.
Immediately after installing and testing the CKEditor plugin, I went back to the Dashboard Plugin page. From there, I disabled the CKEditor plugin and then re-enabled the TinyMCE Advanced plugin. Without performing a browser reset or cache-clear, I attempted to create a New Post and saw that the TinyMCE Advanced plugin was working properly.