There is a 3mm and 5mm glue on edge banding that many cabinet (non-arcade) manufacturers use to finish edges. It's flat, not rounded like t-molding so it won't look much if anything like it but it will provide you with a finished edge of a chosen color. You can likely find some around your house to see what it looks like. Look for a cabinet (again, non-arcade) that isn't made out of solid wood. It's edges will be finished in the 3mm variety and you might find the 5mm on the edges of the doors.
Expensive machines are the normal way of applying this stuff, but some times due to the shape of the board the only option is to glue it on by hand using a high-strength contact adhesive. This does hold up pretty well and look nice when done right. I'm not sure where or if this stuff is commercially available, but it might be something to look into.
