I have replaced the damaged lampshade liner.
The chimney on this shade is like a tunnel. I used a fire retardant on the fabric but the light bulb is the most important factor in keeping the shade safe. In a lampshade with a tall chimney, a candlelight light bulb is the best idea for keeping a safe distance between the liner and the bulb. I used a 25 watt candlelight bulb to light this shade.
Since this in not the actual lamp base for this shade, when I deliver, I will take pictures with different bulbs to see where the actual light comes through on the shade. The pictures will show the glowing point on the shade and determine the correct light bulb to use.