A really weird idea just occurred to me, and while it involves MONEY, it might be the cheapest way to do this:
Cheap web hosting to run the web app with access control + DropGoogleOneDriveBox Cloudy Thingy + Cloud Thingy's API.
Web app manages accounts, user control, access limits, etc. and interfaces through the cloud storage via their API. The web app and the admin are the only ones who can actually access the cloud storage. Because 1 TB hosting is EXPENSIVE, but 1 TB Cloudy Thingy is cheap. So far, I'm only aware of Dropbox and Google who can handle the API's appropriately. Obviously, they will impose transfer limits which we'll have to bring down with us to the web app as we go.
So even if this is a really shitty solution (it comes down to Cloudy Thingy's bandwidth limits through their API), at least it's creative.
Edit: Or I can just pay $2.49 a month for MediaFire and their 1 TB of storage and ability to create what they call a FileDrop: Folders for others to upload into. They also have an API as well and their prices are dirt compared to Dropbox. There were other file hosts and file lockers out there with similar pricing as well.
Edit: I have some Mediafire directories set up. If people need to start grabbing or uploading footage, let me know. Access is granted by email address, so I'll need your email if I don't have it already. Sure beats the hell out of having to write an application.