CableKC

I would just Uber the whole trip.

I tend to use Lyft XL for myself or when my family comes along. Easy and available. RC also does shuttles to/from LAX - you might call them or your TA to find out the cost. 

We used Executive car service out of LAX and we were picked up in a Yukon also outside of baggage claim for $112 including tip. Our driver was very nice, and we will be using him again in a couple weeks. 
 
https://www.executivecarservicelax.com/index.html

There's plenty of Uber that'll will take you from LGB to the cruise terminal.

We used Prime Time Services.  They have many different sizes and types of vehicles, and they were quite decent, beginning to end.  And we've got them booked twice more in the next couple of months. 
Just as an example, we hired a Cadillac Esplanade.  It picked us up right outside the door of baggage claim (LAX), and the price was $118 including gratuity.  They have lesser rigs for less cost, and they have larger rigs.  Call 'em...  They'll give an immediate quote. 
 
https://www.primetimeshuttle.com/services/

I have done both Taste of Royal and the Chef's Table.  Between the two - Chef's table hands down.  Well worth the price!  I would do that again and again.  

We've done Chef's Table twice. The first time we booked on board on a whim, but it was when there were far fewer passengers. The second time we booked ahead so we could get the night we wanted. We enjoyed it very much and will likely do it again on our next cruise.
Pro tip: Book on a night before a sea day. You will be very uninterested in your shore excursion the next morning 😉 

I see both in my Cruise Planner but I'm not sailing on Navigator.
 

Likely they will offer Taste of Royal. Maybe not to book ahead (but check the cruise planner in case), but onboard it should show up in the app.
Also possibly Sushi & Sake. Same drill.

We've done it once. It was fun! It's a luncheon. Here's the menu we had:

We have been on Navigator three times in the last 4 months.  All three times I have been parked in the pier parking lot.  I live 65 miles from the pier and have experienced a Friday morning disembarkation as well as a Monday and Sunday.  If you get off the ship early (7:30am to 9:00am) You may find a bit of traffic with the cargo trucks leaving the docks but I have always made my trip home in under 2 hrs.  Getting thru the RC terminal by taking your own luggage does save time as you can disembark earlier and don't need to search for your luggage downstairs before you go thru customs (Which is quick also).  If your Party can come together in an orderly manner (Not like herding cats),  You should all be outside the RC Terminal  with your luggage no later than 11:30am and ready to get to Long Beach Airport which is about 35 minutes away.
That said, Royal tries to get all passengers off the ship by 11:00am so you all have time to wake up, enjoy a nice breakfast before you leave the ship if you wish and still be outside the terminal before Noon.  Traffic doesn't usually get to bad until 2pm to 3pm on a friday so judge your time accordingly. You should still make it to Long Beach airport within an hour even if your driver takes surface streets.
 
 

We disembarked Navigator on Friday, April 22nd.  We had 11:15am flight out of LAX that same morning.  We walked off the ship carrying our own luggage at about 7:00am.  It took less than 5 minutes to disembark the ship, go through customs, and be outside the terminal waiting for our Uber.  We had to wait awhile for our Uber but were still at LAX a little after 8:00am with plenty of time to spare.  I don't necessarily encourage a morning flight the day of disembarkation, but this example gives an idea of how quickly you can disembark.

Most questions like this are the opposite of yours.  They are trying to figure out if they can get out of the terminal before 8AM!
Not specific to the Long Beach Terminal, but generally the last people off the ship disembark by 10AM.  The ship has to be completely empty of previous cruisers before they can clear the ship to begin embarkation of the next cruise.  That used to start around 11AM but tends to be later now due to extra cleaning.  The worst lines at customs are generally going to be from the rush of people trying get off the ship early and will have died down if you're near the end of the pack.  Overall, I doubt any departing passengers are still around the terminal after 11AM at any port.

You could always do the express disembarkation process; and walk out off the ship as early as possible (You'd need to carry your own luggage); i bet you'd be inside the Shuttle/Uber really fast and avoid any kind of lines. 

2:45 would be extremely late to finish your disembarkation stuff.
 
I have a 1:55 flight out of LGB and I expect to have a couple hours to sit around at the airport.