browser-based 'clients' with large directories and large numbers of files in a single multi-file upload are going to choke. you need binary bits on the parents' end, such as a dedicated backup or sync utility.
if you could populate your server with their existing files using a physical drive, that would be better, and perhaps faster and easier, too--then a browser-based upload solution could probably handle the much smaller 'updates' of new stuff. have them consolidate all the existing files on one external (plus also on a second for a local backup). hell, you could do that bit via remote desktop and all they'd need to do is connect the drives and let you in. then somehow get one of those drives to you (ship, deliver, you pick up. whatever is feasible).