Update from Panopoly 1.15 or older fails with "Table 'drupal.search_api_task' doesn't exist"

The full error:

WD search_api: Undefined data alteration panelizer specified in index[warning]
Database Node Index
WD search_api_index: PDOException: SQLSTATE[42S02]: Base table or    [error]
view not found: 1146 Table 'drupal.search_api_task' doesn't exist:
DELETE FROM {search_api_task} 
WHERE  (server_id = :db_condition_placeholder_0) AND (index_id =
:db_condition_placeholder_1) ; Array
(
    [:db_condition_placeholder_0] => solr_server
    [:db_condition_placeholder_1] => node_index
)
 in search_api_server_tasks_delete() (line 1383 of
/home/travis/build/panopoly/drupal/profiles/panopoly/modules/contrib/search_api/search_api.module).
SQLSTATE[42S02]: Base table or view not found: 1146 Table            [error]
'drupal.search_api_task' doesn't exist

I think it's panopoly_search_update_7005() which is failing, and it search_api_update_7116() which creates that table. I think we just need to add a dependency from one until the other?