Is there a way to configure the startup batch file to recognize if a 'quit' or 'restart' command was used to shut down or restart a server, then run a block based on the command that was used? If so, please let me know how it is done or point me to a resource I can use to learn about it.

I've googled it like crazy but can't find a solution. I am not sure if this simply wasnt thought of for anything but private use or if it is not possible.

I'm not sure you could really do that, but you may be able to find a way to listen to the console output.

Ex. https://stackoverflow.com/questions/20036809/cmd-batch-to-listen-to-output-of-console-application