The cones that go on the spine are part #7 on page 3. The first few I made were lumpy and out of round, because they tended to bend where the slots were cut out.
Are you sure you had to cut slots? I had a good look at the photos from his blog and the one where he shows the construction of those triads there are no slots and part #8 is edge glued on...
I also notice that unlike his prototype in the photos, the seams of the two facing cone parts (#7) do not line up on the bottom (if you did line them up, the lines where #8 attaches will not be lined up). You have to align them using the top #8 (which should be strait up) and the seams will fall where they may slightly off center on the bottom.