I would think that a beachhead would be tied to the ships that supply it. So, lose the CV group and attendant ships---lose beachead. Might mean you need some new ships. GV carrier, Ammunition ship (functions as beachead ords), etc. Maybe these ships would constitute their own task group--with their own escorts. Maybe even Escort Carriers with a limited # of ord-less, fighter only planes---F4F-4, FM-2, A6m-2---. Good question---not sure how it should be resolved---just tossing ideas.
Oh and the GV ship could spawn Amphious Shermans to swim in with the LTVs.