[curt.clifton]

Are you using a custom perspective in context mode? If so, you can:

1. switch to project mode (Cmd-1),
2. configure the columns as you like,
3. switch back to context mode (Cmd-2),
4. open the Perspectives window (Ctrl-Cmd-P),
5. select your perspective in the list,
6. make sure the “Always restore settings for other mode” checkbox is checked,
7. click the camera to take a snapshot of your perspective.

If you aren't using a custom perspective in context mode, the you can use the same sequence to create one. Just skip step 5 (select) and change step 7 to “click the + button to create a new perspective”.

Another approach is to double click a task in context mode to open a new window focused on the task’s project. I think that changes to the columns in that new window should stick the next time you open it by double clicking a task.