The debuff starts once you accept the random dungeon. I've gotten the debuff a few times with the "Additional instances cannot be launched" message. You don't even need to make it into the instance. My routine starts with queueing up for random and getting HoS, then porting my group to H GD and completing it. Then I queue up for random and get HoS again, then port to H CoS and farm the mount. Then queue up for another random and hopefully get one that I can box. If not, off to H UK, H UP, H HoL, H DTK or log onto one of the other groups.