Hosting a remote Aperture image library on a Mac mini server
The approach we have used is a simple shared folder containing an Aperture library. I can report that this solution is ok but fragile -- permissions on the shared folder need to be fixed every so often. 

Dropbox would certainly work in your case, but I suspect that you'll need substantial storage space, which would be rather expensive. If cost weren't critical, though, Dropbox offers a very reliable way of replicating an Aperture library file locally while keeping the copies synced smoothly. Your solution of a GIT repository may be a labor-intensive way of re-creating what Dropbox is already offering.