what POST values are required to update nodes containing CCK Date fields via cURL?
All the CCK fields has access rights settings in actions-roles permission matrix. Normally the access is restricted. Please confirm the permission on date field for your role.

An illegal choice has been detected. Please contact the site administrator. is normally reported when some extra fields are added to the form which are not originally the part of form. It is a security measure from Drupal core.

I do not know how cURL request cycle maintains user session that should be associative with proper role that is allowed to edit date field.