I ended up creating a separate field for each row in the table. Each row was set up as a repeater with 8 fields (one for each column), and then I set the Minimum and Maximum Rows to 1. Then I just duplicated the row and relabeled them so that I had 7 total rows, pre-labeled, with 8 columns of fields.
The interface didn’t look quite as slick as my original idea of using a repeater for the rows but the client was fine with it.
