The material is called a “no fray” fabric, you can buy it at most fabric stores. It will have somewhat more of a weave evident. Getting it in the slot is virtually impossible, add about an inch and a half to length and glue it one full round. All that said, it’s a bear getting it perfectly even, so the next best thing is….
…go to the fellow who restores these for a living. Not terribly expensive and you don’t have to fool with it. About $100 per shade restored.
Heritage Antique Automobile Interiors
1784 Ramblewood Avenue
Columbus Ohio 43235-7332