We completely don't understand this limit nor your explanation that you want to provide fast access, etc.
A 2GB limit sounds almost like from Windows 95 days when you couldn't have a file larger than that. Nowadays, storage (even cloud storage) is cheap, bandwidth is fast and affordable, computing power is available in abundance.
So why do you really still limit the repository size to 2GB?
(A Facebook-style company with a single large repository could never host its source code on Bitbucket. Yet, aren't these the poster-childs you'd like to have as customers?)