Yup, a little metal support will work well there. As you suggest, some small mod of the glass may be required to accommodate the support rod. As Les mentioned, there are many materials that can be used, and thinner materials will help with the glass install. I mention 1/32" brass rod only because I have a bunch around and use it for a gazillion things. A thin strip of pop can aluminum may work as well, though sand the thin plastic coating from the can before cutting and gluing. Many other things can be used, too.