Suggested Workflow Question

I work for a small company with about 15 developers who work concurrently on about 10+ projects both in new development and support. We do custom software for manufacturing and production systems. Part of our contracts with our customers is a perpetual single use license of the source code at each facility. So we have a copy of the source on our office server, and another copy at each customer site. When we had only 5 developers it was easier to handle. Now that we are growing we need a source control system and I have been looking heavily into Git. Our old workflow does not seem that it will fit well with Git however, but I feel that I need a distributed system to keep track of the office version and the on-site versions of our source since development is taking place on both. (Some customers also have separate development, and testing versions on their servers as well.)

I have created git repositories on a couple of our project source directories as
test beds.  Right now (second day) I am the only one who is actually using git.
 Everyone else is simply accessing the files on the server as they have always
done, and I am making the commits when I see signifigant changes. 

My question is really a request for modified workflow ideas. My plan was to have a master repository in our office server with clones at each customer site, and multiple branches for test, QA, and production versions of the source. Since most of these customers have closed networks, we would rely on people traveling onsite, or emailing patches to get any updates back into our office repository.

Thank you for any assistance for this revision control newb.

Roger Garvin