Or how about 999 additional computers? They could be really tiny ones, running some kind of operating system designed for putting inside small single purpose machines. You could also add a coloured light on the front of each one and a button that says "copy to NAS".
Or each SD-card-reader node could copy to its own hard drive (to free things up for another card) and asynchronously upload from there to the central unit... Or possibly send metadata/thumbnails first, and then alternate between sending specifically-requested content versus uploading the backlog.