Not to mention this bug:
UPDATE
OK, I almost have it. I set the very top Div in each section with a relative position and a z-index in descending order. It was necessary to set both in every section, even though the top most parent div is NOT the parent transformation target.
HOWEVER! I cannot get more than 3 of 4 transformations to work. 
For example: If I set all the sections to relative, and set the z-index for each of the sections the following happens:
All Z-Index the same: Only top (swirlberry) fails.
Z-index in Ascending order: Only top (swirlberry) fails
Z-Index in Descending order: Only bottom (blurberry) fails.
What the hell?? 