Is there a standard way or a recommended way of dealing with this in Java EE?
I'd use a real integration layer (as in EAI) for this purpose, running as an external process. Integration tools (ETL, EAI, ESB) are specifically designed to deal with... integration and many of them provide everything required out of the box (simplified version: transport, connectors, transformation, routing, security).
Basically, when dealing with files, a file connector is used to monitor a directory for incoming files which are then parsed/split them into messages (applying optionally some transformations) and sent to an endpoint for business processing.
Have a look at Mule ESB for example (has a File Connector, supports many transports, can be run as a standalone process). Or maybe Spring Integration (coupled with Spring Batch?) which has File and JMS Adapters too. But I don't have much experience with it so I can't really say anything about it. Or, if you are rich, you could look at Tibco EMS, WebMethods, etc. Or build your own solution using some parsing library (e.g. jFFP or Flatworm).
Is there an application server specific way around this?
I'm not aware of anything like this.
Can you justify breaking this process out of the application server? And how would you design the communications channel between these two separate systems?
As I said, I'd use an external process for the file processing stuff (better suited) and send the content of the file as messages over JMS to the app server for the business processing (and thus benefit from Java EE features such as load balancing and transaction management).