Found a solution.
I’ve set it up so that that wp-admin is always loaded in to SERVER1. Once a user has uploaded files using WordPress into SERVER1, I rsync wp-upload to SERVER2.
The key was making sure that wp-admin is accessible on 1 server that is being load balanced.
Once we have a need to use a CDN to serve wp-upload items, I would only have to modify the $siteurl to point to the CDN url for the upload’s base url (wp_upload_dir function).
Thanks for the other suggestions.