Hashing the filename doesn't help, the URL is different, which is why caching doesn't work.

If we ignore that ETags are related to URLs and not 'files', ETag as suggested by userbinator might work for some cases, but if the large file is dynamically generated, it's unlikely to have an ETag; defaults in many servers are to make an ETag based on the inode of the file rather than any properties of the file, so if there are multiple servers behind a load balancer, they're likely to return different ETags.