Wow, now that's support!
Thank you Rik for your insight. I thought 11 shots would be enough for this subject as it was a few centimeters long, however the aperture was probably a bit wide looking back. The MPE-65 lens I've used here is very new to me, I'm still learning the ropes. I may try this shot again when I find another poppy seed, I've got a much better working setup now than I did then, and a little bit more experience under my belt. I'm sure that you're right in that a good part of the poor results here was from my own inexperience.
I'm currently working on another image stack and have similar problems, though not nearly as pronounced. Will post results another day.