I finished the spiral pineapple doily, finally.
The end of this pattern gave me fits. It was just wrong wrong wrong. Each of the pineapple tips is worked separately back and forth, and the pattern says that there are supposed to be chain-8 bridges between the pineapple and the double-crochet shells along the sides. I did a couple following the pattern, but it quickly became obvious that this wasn't going to work. The ch-8 bridges were too long and floppy, and the whole tip cupped horribly. If you scroll back to July 9, you can sort of see this on the one that's done. I test-blocked the two tips that I had done, and realized that no amount of blocking was going to help this. So rip those two tips out. I figured that since the ch-8 bridges were too long, if I just shortened them it might work. So I redid one tip using ch-5 bridges. Alas, still no good. Still severely cupped. Rip, rip.
After thinking about it I realized the reason the tips were cupping was not that the bridges were too long, it was that the double-crochet shells at the sides were not able to stretch as much as the pineapples in the middle. The bridges were the right length for the pineapples, but the outside edge had much less "give." So I redid a tip using TRIPLE-crochet shells along the sides this time, and lo and behold, it lays flat!
So the bases of the pineapples, the part worked in the round, have double-crochet shells and the tips have triple-crochet shells. It's not too noticeable, and since it's the same all the way around the doily, it looks fine.