So many options, so little time! 9 days in Croatia

Do not miss Plitvice!

Frankly, I’d spend more time in Split, and surrounded by area, than Dubrovnik.

Yes you are doing too much. It isn’t easy or fast getting from city to city in Croatia. Some ferries only run once a day and not always at a convenient time. With the time you have I would cut Korčula and just concentrate on Dubrovnik, Split and Plitvice. I would stay two nights Dubrovnik, drive to Plitvice and stay overnight, drive to Split, return car. Three nights Split with day trip to Trogir or Hvar, then ferry back to Dubrovnik for two nights. Check catamaran schedules at Croatiaferries.com or go directly to Krilo.hr for schedule and booking. You can ferry to Trogir (1hour) and to Dubrovnik (4.5 hours).

I would suggest staying in Split the first two nights after arriving in Europe. Then either take a bus (3.5 hours) or drive a rental car (2.5 - 3 hours) to Plitvice Lakes National Park where overnighting at one of the three hotels inside the park entitles you to buy a “ one day ticket” for admission. The “one day ticket “ gives you admission to the park both on the afternoon you check in to the hotel ( either the Hotel Plitvice, the Hotel Bellevue or the Hotel Jezero) and also the following morning. These are the times the park is least crowded with all the tour groups arriving about 10:30 am and departing about 3pm.
Return to Split and depart on an afternoon Krilo Catamaran for the 75- minute ride to Hvar where you can overnight for one or two nights. Take the Krilo catamaran to Korcula (1hr at 8:15am, 11:15am and 5:50pm) and overnight there before continuing to Dubrovnik ( 2- hr ferry ride) for the final two nights.
The alternative routing and driving directly to Split after landing in Dubrovnik would mean a 3-hour drive.
I don’t think I would attempt driving a rental car immediately after a transatlantic flight, but if you are comfortable with the idea, you can rent a car at Dubrovnik’s airport and drive to Plitvice Lakes National Park. It’s a 5-hour drive so overnighting in a small town on the way to Plitvice makes more sense than going into metropolitan Split. After Plitvice Lakes, you can drive to Split where you can return the rental car to a rental lot in town in Split. You won’t need the car in Split or for any of the rest of your itinerary.

The ferry and catamaran schedules might help you make a loop:
https://www.krilo.hr/en/
https://www.jadrolinija.hr/
I would probably not include Plitvice since you have to return to Dubrovnik, but easy for me to say--I've seen it! Krka involves less travel time.
On arrival, you could head directly to Split (I would take bus so I could nap) or to Korcula. There is a shuttle service called Korkyra, it goes from the airport to Korcula, so that might be an option.
I would give Dubrovnik the least time after Plitvice because it is very small--that is, unless you have lots of day trips planned.
One sample itinerary:
Arrive Dubrovnik, shuttle to Korcula (or bus or catamaran)
two nights Korcula, catamaran to Split, pick up car and drive to Plitvice, one night Plitvice
hike in Plitvice afternoon and following morning, then return to Split, split remaining time between Split and Dubrovnik.