Thanks for taking time to look at my issue!
I think I resolved it! The problem was between my chair and my keyboard.
TL;DR: Export and Run only works on the first instance of Maya you have open. If you initiate a Export & Run in a single instance of Maya, it seems to lock that feature to that instance. I needed to close out all instances of Maya. Reopen the file and use the Export & Run Feature.
I close out all open instances of Maya
Open Maya > Create cube > Set File Name > Export & Run
The Export & Run button is available and works.
If I Open a second instance of Maya, The Export & Run button is gray/disabled.
If I close out the first instance of Maya and leave the second instance open, the Export and Run is still gray.
I needed to close out all instances of Maya, particularly ones where I had used the Export & Run feature. Then only set up one instance of Maya where I am using that feature.