The function of the tools I use and how they work are explained here. Specific tools used are noted in bold.
New glass retaining strips that hold the glass in place in the mullions (wooden cross bars) are made from mahogany to match the door exterior. The original curved strips are cut from a solid piece of wood, but this results in sections that have end grain, which is not very strong. As a better alternative, I made the curved strips by bent laminating two twin pieces of mahogany. The two pieces are epoxied together, and clamped into a form to dry. This results in strips with the full long grain along the entire strip.
When the door was sanded the outer edge of the mullions was sanded off. New mahogany pieces are glued in place to match the door plies.