The only thing I can think of doing is to take the completed liner and insert a smaller tube into it snuggly. Then apply the glue to the outside of the liner. Make sure the liner is longer than needs be. insert the smaller tube into the tube and make sure you "catch" the other end. Then try and twist it around so it will cling to the insides. When you think it has taken then slide the smaller tube out. Maybe that will work. Good Luck.

What about making a tube about twice the size you need with a little extra for sewing or gluing. Push your tube through the pipe and pull the tube back over the outside of the pipe. Sew the edges together so it stays permanently or you can sew the end together so whatever doesn't slip out that end. The tube won't be glued to the pipe, but it will still cushion.

Why not make a tube with the felt, sew the long seam, then push into the PVC tube. Glue the felt to the PVC tube at the top and bottom. I see no reason to glue the felt all the way through the PVC tube.
Kathy G in MI