An older TV required about 15 seconds. It was ridiculous. In that control system I could start the TV power ON-input select command string running in the background and allow the user to move on to select a cable channel while the TV was still booting up. Eventually the TV would catch up. I don't know if Harmony supports this or if this will resolve your issue.

What inputs are available for the TV? You may be able to turn things inside out by starting another input device that will send a power command to the TV via CEC. If this is not the final device that you want to view, send an appropriate input command after the TV finally starts.