@getcooking - your pattern of Panda hits is very similar to ours...
We were hit and Panda 1.0 and thereafter. We experienced a 15% recovery at Panda 3.6 (apr27, 2012). This was then taken away at Panda 3.7.
So the question is what caused the small recovery. Its too hard for me to tell as we've made so many changes across the board.
As for what caused the Panda 3.7 hit, we made a design change in early May that included a small sidebar with 20-30 links to our best pages. This is the only major change, could this have lead to another panda hit (too many links on page)?