Thank you all for your suggestions and input, I appreciate it!
Our flight was rescheduled to arrive even later, now won't be landing until almost 11pm so I was really second guessing the hotel in Miami. I kept checking and a room at the Hampton Inn near the airport in Fort Lauderdale finally opened (we only book Hilton chain hotels bc of the ability to use points or book at very low employee rates). We cancelled our room in Miami. There is a free shuttle running from airport to hotel that runs until midnight. If we don't make it, we will try uber for the first time. We booked private transportation with Larry's Limo to get from our hotel to port the morning of the cruise. Post cruise, we will take the free shuttle from port to MIA to pick up a rental car from Alamo for our 2 days in Hollywood. I've read that pickup is easier there than near port. We will return the car at FLL the morning of our flight home. All said, transportation will cost $233 (if we catch the hotel's free shuttle). And it seems relatively hassle free.
For any others who might be planning to arrive in FLL and travel to Miami late at night as we were originally planning to do, Jiffy Jeff's does offer a shared ride with pick up from FLL after 3pm, but charge a higher rate to do so. Our quote was $135 (as opposed to the $60 it would have been before 3pm). We also had a quote from Larry's Limo for private transport that night and it was around the same price as Jiffy Jeff's. FG Car services never responded to my quote request. A one way rental from FLL to be dropped off near port the next morning was $68 with parking at hotel. The idea of getting the car after our long flight, then trying to find my way around Miami at midnight, then fighting the crowds to return the car the next morning and waiting for another shuttle to port just was not appealing to me. A rental car for the entire week to pick up and drop back off at FLL plus parking at the hotels and port was $430.
I feel much better about our current plans. Thank you all again!