Something I commonly do in my projects is go hunting for which windowCOMP is set to perform, and open it on the destination monitor as a preview.
This or I bind the parameter to a project comp and then have to search for that pulse button.
Built a shortcut today to use Shift.F1 to find the project.performWindowPath op and just open/close that window.
Seems like such a basic impulse for key control that could be added to the application keyboard shortcuts list for others.