Since making the lamp, I have found some suitable paper. I was looking for something that was transparent enough to allow light through, but not to the point where I could clearly see the bulb. Vellum paper from Michaels fit the bill.
I made a pattern using cheap printing paper (that stuff can really mess up your printer, but works fine as pattern paper) and cut the vellum when I was kinda sure I had something that would work. Of course, I had to wait for a day when I felt I would have an infinite amount of patience so I wouldn’t destroy the lamp altogether. I used double stick tape at first to hold pieces together and when pieces began to fall off after some weeks, I used a hot glue gun. It isn’t perfect, but I have promised myself I will do a lot better with the other one.