Try this:
First, turn off "subtasks in order" on all your projects - in my view this just complicates things.
Then, start with the All Tasks view. If you think you may have changed the All tasks view, create a new workspace and experiment in the new one for a while.
Change the filter as follows:
General>show actions>next actions
General>Show Hierarchy>Yes
General>Show Hierarchy>Config>Parents:yes(no filter)>Children:no>Highlight>no
General>Show Completed>No
Group&Sort>Group>none
Group&Sort>Sort>computed-score
Then right-click on the column headings to get a list of available fields. Uncheck any that are displayed but uninteresting, and check off Importance and Urgency.
Save the view and give it a nice name.
This may not be what you want - your needs seem to be quite complex. But this is a pretty simple view (no advanced filters) that shows only those tasks that are next actions for some project or folder, shows the project names as well, ranks the projects in order of their importance and urgency (not really - it's the computed score of the next action, but if subtasks all use the default importance and urgency it works out pretty much the same as using parent importance+urgency), projects do not disappear when they have no active subtasks, project importance and urgency are visible and editable, a task that is not in a project is still visible but only if it is the next action for a folder that it's in, if you postpone a task from this report (future start date) it falls off the list and is replaced by the next available task in the same project (if there is one). It was a little tricky figuring out how to do your "forced second next action" thing but here's what I came up with: Find the task you want to force as a next action. Just above it as a subproject and move the task into it. Maybe you want to move several tasks into the subproject so that when one finishes the next will take its place in the report.
If there are tasks you wanted in the report that are missing or that are showing on the report but should be hidden, please try to describe the precise test that will validate the conditions that determine why this task should be shown or hidden.