Would keeping Jellicoe at the Admiralty improve the design?

Would leaving Jellicoe as Third Sea Lord for a few more months have corrected other Queen Elizabeth design problems?

Possibly. It might also have delayed the promotion path that made him Grand Fleet commander, so the institutional gain carried an operational cost.

Jellicoe might have pressed for other engineering changes if he had remained Third Sea Lord for a few more months. Remaining in the construction post could also have delayed the promotion path that put him in command of the Grand Fleet. The later Royal Navy tried to preserve continuity by promoting an important Third Sea Lord in place and arranging sea time around the office. Design oversight therefore had to be balanced against preparing senior officers for operational command.