Do you have luggage to check? Hopefully you do have TSA precheck.
the tunnel is open from Whittier on the hour, 7am, 8am, 9am, etc.
11:15am departure means a 9:15 check in which means having the bus transportation leaving Whittier at 8:15 ( leaving, not boarding the bus). I could be wrong but I would say it is highly unlikely that any Princess transport would make the 8:00am tunnel opening which then puts you back to 9am, possibly arriving in Anchorage sometime after 10:00am.
Jenny