After a more careful look at the logstash internal logs, it looks like it was looking for '/usr/share/logstash/config/log4j2.properties'.
After renaming the .properties file to include the '2', the internal logs now say:
Sending Logstash logs to /var/log/logstash which is now configured via log4j2.properties
However, the log files are not appearing in /var/log/logstash. I've used chmod to give full accessibility to this folder in case logstash simply didn't have the permissions to write files in this folder, but that doesn't seem to help.