There were definitely more than two USN Phantom squadrons in 1982 because both Coral Sea and Midway had them and they were still deploying on some of the bigger decks as well in the early 1980s plus there were the USMC squadrons. The F-18 did not deploy with a carrier until late 1985 (Connie) and did not see service on Coral Sea and Midway until 1986. I think there is a general misconception that the F-18 entered operational service with the CVWs a lot earlier than it really did (the RAGs don't count, obviously they were in service with those earlier). Most CVWs did not swap out their A-7s for F-18s until 1988 or 1989.Something that hasn't really been addressed with all the talk about having an Essex operate Phantoms is that the VFX programme selected the Grumman 303 in January 1969 to replace with Phantom. The first Phantom sqns converted to the Tomcat in 1974 and IIRC by about 1982 there were only 2 Phantom sqns left on carriers, so keeping Essex's in commission is shakleing the USN to either the very old F8 or old F4.
Before anyone starts crowing 'F18', that comes with it's own significant issues. The USN primarily replaced A7 sqns with F18s, IIUC only 2 F4S sqns were replaced with F18s, it was the USMC who were the big user of F18s in the fighter role, replacing USMC F4 sqns. The mid 80s deployments of Midway class carriers with F18s were 2 USMC sqns in the fighter role and 2 USN sqns in the attack role. There were a few deployments in the early-mid of CVWs with 2 F14 and 2 A6 sqns because A7s sqns had converted to F18s but these ships (including JFK in 1983 when it bombed Lebanon) hadn't had the refits needed to operate the F18. So if Essex are retained into the 80s with the idea that the F18 will fly from them they will need significant refits to operate this aircraft.