Batch processing possible without redirects?
Redirects work just fine if your infrastructure is set up correctly.  I will assume your issue is that you have a mount point for your public files directory - but not for your temp directory?
If you don't want to make two mount points (three, if you have a private folder), instead have one and just have three folders inside for tmp/ public/ private - then symlink tmp and public (e.g. tmp to /tmp/drupal).
The reason being is that file processes create temporary files which then can't be used by other instances if they're not shared.  The external page cache isn't a factor here as it doesn't care so much about any of this, and I'm going to assume that this is for authenticated users too - so it's actually being bypassed (further assuming it's set up correctly). The load balancer cares even less, it just bounces you between instances unless you're using sticky sessions.  Every instance should have access to the same database, files and cache - there won't be any problem.