I'm not sure if a method to execute a system task has been added to the API since this post, but I also ran into the need to do this. In my case, I needed a way to programmatically create chart objects for chartless documents that would never get resolved because they will never receive the HL7 data to create a chart object for them.
As a workaround, I wrote a Unity script that (1). queries the database for the documents I wish to process and (2) adds them to a lifecycle that performs the work I need done (sends an ADT A01 mesage to the localhost for each document).
To provide a way to execute the script in the GUI, I created a dummy document type called "Workflow Script Trigger” and also a dummy lifecycle that does nothing but run the script. Then, I created a dummy system task for the dummy document that adds it to the dummy lifecycle. When I need to run the process, I just open the document and click the dummy system task.
I am not sure if there is a more elegant way to handle this but it meets my needs.
