Event importer shows only one target content type per date field

I am attempting to convert from the Event module to Date/Calendar. I have several Event-supported content types, and I would like to copy those dates in-place into a date field. I have created a single event_date field and added it to all of the content types in question. However, when I go to Date Import->Events, only one of the content types containing that field is shown in the Target list, preventing me from copying the dates in more than one content type.

If I remove the event_date field from the type that is shown in the list, another type that has that field appears in the list to take its place. It would appear that the target list is showing only one content type per date field type, rather than showing all types that have each field. I am new to Drupal, but tracking down what happens in the date_copy_type_form() function seems to corroborate this. For each date field it pulls just one type name from $field['type_name'], rather than finding all types that use that field.