I did something similar but I called it "follow up". So when a ticket was, in your case, suspended it would be given a priority of "Suspended". Then it would be moved to a separate list. For example...
At the top of the screen, next to the "open", "overdue" (etc.) categories, you could add another one called Suspended.
As far as getting rid of the aging of the ticket. That might be handled in include/staff/tickets.inc.php but that code is such a train wreck I don't want to look through it at the moment. You could just have the open and overdue list not show priorities of suspended. Therefore, all suspended priority tickets would only show up in the Suspended area.
Hope that makes sense.