I read that these ships are supposed to go to the late 2030’s, but a modified LPD might be a good choice.The USN needs two or three ships to serve as flagships for numbered fleet commands. I'm not aware of any plan to replace these two ancient LCCs. Maybe a modified LPD?
USS Midway CV-41 (now a magnificent museum in San Diego) is a great example of how a ship can be modified and updated to handle new technology. Commissioned at the end of WW2 in 1945 with Helldivers and Corsairs, she served through the Gulf War finally being decommissioned in 1992 handling Hornets and Tomcats. During that time she went from a straight deck carrier of 45,000 tons to a catapult equipped angled deck carrier of 65,000 tons.

With reports of China now building up to 9 carriers and thus the need to maximize our nuclear carriers in the Pacific, could the big America class gators undergo a similar upgrade to handle other theaters with either tailhook manned aircraft or drones?

USS Midway steaming off the Firth of Clyde in September 1952.

Midway en route to Southeast Asia in April 1972

Midway departing Yokosuka for the last time in August 1991