Any chance of getting some more samples of the controller output please? I know you said that the controller sends a burst of data then goes quiet but are the couple of examples you posted the entire output of one controller program select or just a subset?
EDIT: More questions,
If you listen to the DAT/CLK lines when the unit is doing a chase (assuming the controller does this) is the data continuous/repeated between controller and first chip and if not what about between nth & nth+1 chips?