Another clue...
With just one column heading object and one column data object (rendering correctly,
with just one record in the output cursor), the method calls are as follows:

EvaluateContents - Col 1 Head
BeforeRender - Col 1 Head
AfterRender
EvaluateContents - Col 1 Data
BeforeRender - Col 1 Data
AfterRender

When specifying two columns (i.e., 2 heading objects and 2 column data objects), I should get
the same threesome for Col 1 Head, Col 2 Head, Col 1 Data, Col 2 Data. Instead, I get --
EC Col 1 Head
EC Col 2 Head
BR Col 2 Head
AR
BR Col 0 Head
AR
EC Col 1 Data
EC COl 2 Data
BR Col 2 Data
AR
BR Col 0 Data
AR

In other words, I'm getting the right number of each method call, but in the wrong order.
(The "Col 0" I ascribe to the nColumnNumber prop being reset at the wrong time.)
Hmmmm...