I've been in a similar situation a few times. For starters, hotel's shuttles/buses tend to work all throughout the day. Keep in mind that their main purpose is to take guests to and from airports as well as cruise ports. So it's highly unlikely that the latest their shuttle travels is 11am. Maybe 11pm (night), but definitely not 11am.
That said, you need to contact the hotel and ask two simple questions.
1. Do they offer late check-out and if so what's the surcharge?
2. What time(s) does the hotel's shuttle go to the port?
Late check-outs is usually around 2 or 3pm, but some hotels will even go to 6pm depending on how full they expect to be. So definitely inquire. This will likely incur an additional fee, so ask so you're not surprised.
In most instances, if you tell the hotel your situation, they'll do quite a bit to help accommodate your needs, especially if they're as simple as what you have going on. But please contact them as early as possible, that way when the time comes everything is in place to accommodate you and those traveling with you.
