What about using a servlet container lifecycle listener, such as ServletContextListener?
Example on how to use.
EDIT: Sorry, after re-reading your question I don't think this will work. You want something that will load only once per server life, not application life. The ServletContextListener's methods will be called each time the app is deployed, just like a load-on-startup servlet (which it seems you are using). My suggestion will do the exact same thing in a different way.
I would try Chris Nava's suggestion.
EDIT2: It looks like tomcat has some lifecycle listener(s) available to it also. It looks like documentation is sparse, but this potentially would allow you to do something on server startup specifically only once.
EDIT3: Yes, a tomcat lifecycle listener is the way to go. This link explains pretty well how to set one up. Should be fairly straight forward. If you ignore the part about adding the Transaction to tomcat, it goes over pretty thoroughly how to add a lifecycle listener.