GIT as binary repository

Hello, 

We are investigating the use of GIT as a binary repository solution. Our larger files are near 800MB and the total checked out repo size is about 3 GB the repo size in SVN is more like 20-30GB, if we could prune the history prior to MR, we could get these sizes down considerably. This binary repo is really for our super project build.  From what I have read and learned, this is not a good fit for the GIT tool. Have there been performance improvements lately? Some of the posts I have read have been quite old?

I also have some questions, about how the workflow would be for getting all of the changes merged from several different teams into the one repository would operate. Do we setup a shared system for engineers to perform the merges onto? Our teams are geographically disbursed. 

Thanks for any light you can shed on this. We are trying to digest a lot of information quickly, so sorry if there are things covered here that are elsewhere.

Thanks, Kevin