I think you might want to put on an external stem, that way you don't need to worry about getting a nice tidy, sharp point based on fitting all the strips from both sides together. Just fit the strips tight to each other on both sides and cut them off close to the internal stem or form so that they don't interfere with the strips you are adding on the other side. When its all stripped plane the ends flush right down to the internal stem or form. Then glue on a series (three or four) of thin flat (