How to create a web page for uploading very big files to OpenStack Swift?

I would like to set up a web page where a user could upload very big data files to OpenStack Swift. The data files have file sizes that sometimes exceed the object file size limit of Rackspace Cloud Files (5 GB). This seems to rule out the possibility to use FormPost for uploading the input files. Quoting the Rackspace Cloud Files documentation: If your users try to upload an object larger than 5 GB, they will get a file size error

How could I set up a web page where a user could upload very big data files to OpenStack Swift? We currently use the OpenStack provider Rackspace and their Open Swift service called Rackspace Cloud Files.

FormPost would have been a great solution as it doesn't rely on sending the data files through my web server. With FormPost the data files are being sent directly to Rackspace Cloud Files.

As a good general security permissions strategy, I would also like to find a way where I would give the user as little Rackspace permissions as possible.