It is possible to do this project with the 15/0 charlottes, but it's not as easy as with 15/0s or 15/0 cylinders. If you look at photo b on p. 61, you can see one of the earrings I made to test the instructions. I did use 6 lb. test Fireline. Have you tried a #13 needle?
I have to admit, I break 15/0s all the time when I use them with Fireline, but when I try other threads, I break the thread. I break needles on 15/0 Charlottes more than any other type of bead. I think the root of my problem is that I bead very tightly. It's a pain to have to unravel work and replace the broken bead, so I understand your frustration.
Two things that help me (most of the time):
• I try to leave a little slack in the thread when I know I need to go through beads again. If I can move the bead a little, I can maneuver my needle to a better angle, and it can pass through the bead more easily.
• I pay attention to the size of the hole, and try to use beads with larger holes.
Did the project work out for you, using the 15/0 cylinders? I imagine that they would be much easier to work with.