For the past few years we have been using a Linux SMB file server,
located within the office LAN, to host all of the project files. It
works well because it is fast enough that I can mount the SMB share on
each workstation, and users can access/save the drawings directly. This
way, there is no need for a check-in/check-out system. We are
building new offices in some remote locations and will need to come up
with a new solution that will allow users anywhere on the internet to
collaborate and work on the same projects. The office will have a
dedicated fiber connection with 3mb/3mb and 5mb/5mb burst throughput,
so some kind of server located within the office may be a favorable
option. A VPN might be too slow for users to work directly on the
server from a remote location in the same way that they do now with the
SMB server. I have heard that Microsoft Sharepoint was notoriously unfriendly with CAD programs because of the way they put locks on files. I looked at Autodesk's Buzzsaw this week, and signed up for a free trial. It
looks attractive to me because it is designed to work well with CAD
programs, handles check-in/check-out, and includes a version-tracking
feature. Can Buzzsaw be installed on a local server? Can I install
it on a file server in one of my offices, and then serve it to the
users in other offices, or am I stuck to having Autodesk host
everything? Does anyone have any opinions about this product in
general? Is it quirky and linear, and will it prevent me from doing
something strange? Will it work with non-Autodesk products like
BricsCAD? I am open to any and all alternative ideas. I have met someone who has written custom code for a check-in,
check-out system; someone who has set each employee up with his
personal project folder so that he couldn't overwrite anyone else's
work. How is your remote office set up?

Have you looked into Autodesk Productstream?  It should allow you to do what you need to do.