No, there is only one instance of AS 7.1.  There are N instances of my application running on the single AS 7.1 server instance. Thus, I have something like /myapp-cust1, /myapp-cust2, ..., /myapp-custN. 

To kind of explain further what we're doing today, we currently have an ANT task for each customer that fills in the appropriate customer-specific value for the properties file and then packages up the WAR file.  This means we deliver N-number of WAR files to the operations team to deploy.  When we get a new customer, it means adding a new ANT task for that customer.  Something about the whole process just feels wrong.  It's not currently possible to deploy this application if we get a new customer without involving the development team so that they can add the ANT task and build the WAR file.  It also means that the location of the properties file is something that is fixed once the WAR file is built unless the operations team wants unpack it, change the context parameter value, and then package it up again, but that also seems like a pretty bad practice.