Converting a theme to a child theme in a network

Figured it out. Sites have three options in the wp_options (or wp_n_options where n is the blog id) table. You can see them by running:

SELECT    * 
FROM      wp_options 
WHERE     option_name IN ('current_theme', 'stylesheet', 'template')

To fix blogs after replacing a normal theme with a child theme of the same name, run an update on the wp_options table for that blog, setting the template option to the parent theme path:

UPDATE    wp_options 
SET       option_value="parent-theme-path"
WHERE     option_name="template";