A certain form in our application displays a graphical view of a model. The user can, amongst loads of other stuff, initiate a transformation of the model that can take quit
I think your folly is thinking of the transformation as a single task. If user input is required as part of the calculation and the input asked for depends on the caclulation up to that point, then I would refactor the single task into a number of tasks.
You can then run a task, ask for user input, run the next task, ask for more input, run the next task, etc.
If you model the process as a workflow, it should become clear what tasks, decisions and user input is required.
I would run each task in a background thread to keep the user interface interactive, but without all the marshaling issues.