How can I make an order generated through Services invoke hooks or checkout complete? I am stuck at integrating a Drupal Commerce store with Services.

I setup a REST server. In several steps I can login, create a user, create user shipping/billing profiles, create an order, add line-items to that order. This works fine, even a correct total gets calculated. I then need a bunch of rules and some hooks to get triggered to make invoicing happen and to send out emails. This fails. I tried to trigger this by changing the order status. Maybe I haven't done it right.

Drupal 7 Modules I use:


Services
Commerce Services
Services Entity


How can I make a D7 Drupal Commerce order generated through Services invoke hooks and rules? To make it simpler: How can I invoke the checkout complete process through services?
So, for anyone looking for a solution, here is what I did after asking for help in IRC #drupal-commerce:

Don't use the order status, don't use a checkout-status. Use something (an entity) as a trigger that is necessary for creating the order. I picked the last action provided via .json-file, POSTing a line-item. As soon as this is known by Drupal, all corresponding rules start their work, and some hooks respectively. 

Sidenote: I learned something else also and wished to have been pointed to that earlier: Next time I will not use the above mentioned modules again. They're buggy and obsolete in D8 anyway since the concurring RESTws module became part of core.