What I can do:
I can drag & drop a subtask off of it's parent and make it a task at the same level as it's former parent. I can then attach this task as a subtask on a new parent by going through the "Turn existing task into a subtask" option.
What I would like to be able to do:
I would like to be able to drag a give subtask to a new parent task in one action via a simple drag & drop. This would detach it from the original parent task and attach it as a subtask of the new parent